Intro to Statistical Reasoning
Intro to Statistical Reasoning STA 1043
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Chapter 01 Collecting Data In Reasonable Ways TRUEFALSE 1 N w 4gt U1 9 gt1 00 gt0 i O The entire collection of individuals or objects about which information is desired is called a sample ANS F REF Section 11 AP A study is an observational study if the investigator observes the behavior of a response variable when one or more factors are manipulated ANS F REF Section 11 AP By de nition a simple random sample of size n is any sample that is selected in a manner to guarantee every individual in the population has an equal chance of selection ANS F REF Section 12 AP Response bias can occur when responses are not actually obtained from all individuals selected for inclusion in the sample ANS F REF Section 12 AP Selection bias can occur if volunteers only are used in a study ANS T REF Section 12 AP Stratified sampling is a sampling method that in no way involves simple random sampling ANS F REF Section 12 AP Increasing sample size will generally eliminate bias in a sample ANS F REF Section 12 AP As long as the sample size is small relative to the population there is little practical difference between sampling with replacement and sampling without replacement ANS T REF Section 12 AP Clusters are non overlapping subgroups of a population that have been identi ed as homogeneous ANS F REF Section 12 AP Random subpopulations of a population are called strata ANS F REF Section 12 AP AP and the Advanced Placement Program are registered trademarks of the College Entrance Examination Board which was not involved in the production of and does not endorse this product 446 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 11 Blocking is a technique that can be used to filter out the effects of extraneous factors ANS T REF Section 13 AP 12 A placebo is identical in appearance to the treatment of interest but contains no active ingredients ANS T REF Section 13 AP i w In a well designed experiment the factors are confounded whenever possible ANS F REF Section 13 AP 14 A treatment is any particular combination of values for the explanatory variables ANS T REF Section 13 AP i U1 Two factors are extraneous if their effects on the response variable cannot be distinguished from one another ANS F REF Section 13 AP 16 Random assignment to treatments will guarantee groups that are exactly alike for experimental purposes ANS F REF Section 13 AP 17 The method of control wherein an extraneous variable is held constant is called blocking ANS F REF Section 13 AP i 00 A control group provides a baseline for comparison to a treatment group ANS T REF Section 13 AP 19 Random assignment of volunteers should result in comparable experimental groups ANS T REF Section 13 AP 20 1f the subjects as well as the person measuring the response are aware of the treatment assigned to the subject only single blinding is being used ANS F REF Section 13 AP 21 Replicating in an experiment means that the number of subjects is greater than 1 ANS F REF Section 13 AP 447 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part MULTIPLE CHOICE 22 Which of the following statistical studies is an observational study E A group of students is surveyed to determine the percentage who believe in reincarnation A random sample of students is shown a documentary on the evolution of reincarnation beliefs throughout human history A second random sample is not shown the documentary The object of the study is to determine whether viewing the documentary affects belief in reincarnation c To determine whether Vitamin C has any effectiveness at lessening the duration of the common cold one set of cold sufferers is given no Vitamin C a second set is given 2 grams per day and a third set is given 5 grams of Vitamin C per day 9 d All of these studies are observational e None of these studies is observational ANS A REF Section 11 AP 23 Which of the following statistical studies is an experimental study a A researcher observes the effect of alcohol consumption on reaction time by administering various quantities of alcohol to randomly selected subjects b A study is conducted to see if exposure to increased carbon dioxide levels increases tomato yields Tomato plants are selected at random and are then exposed to various doses of carbon dioxide c Two random samples of senior adults are selected The first group watches a 30 minute presentation on Medicare fraud while the other group does not watch the presentation A survey is then administered to measure the level of confidence the subjects have in their health care providers d All of these are experimental studies e None of these are experimental studies ANS D REF Section 11 AP 24 Select the correct sampling method for the following situation To analyze the level of employee satisfaction at stores in a certain large city a grocery store chain selects eight store locations at random and surveys all employees at these locations a Simple random sampling b Stratified random sampling c Cluster sampling d Systematic sampling e Convenience sampling ANS C REF Section 12 AP 448 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 25 A study is commissioned to determine whether piglets gain body mass more rapidly when a certain hormone is introduced into their feed In January a random sample of40 10 week old piglets receives a diet that includes the hormone Sixteen weeks later the average weight increase is determined A similar experiment is conducted the following June with a random sample of 36 piglets except the hormone is removed from the diet Which of the following do you think represents the most serious flaw in this study 994165 E U 9 F 965 99 the presence of a confounding variable the presence ofa sampling bias an absence of experimental control the presence of a measurement bias inadequate information regarding dietary needs of piglets ANS A REF Section 12 AP Which ofthe following statements is false The explanatory variables are those variables that have values that are controlled by the experimenter The response variable is the variable that the experimenter thinks may be affected by the explanatory variables An experimental unit is the smallest entity to which a treatment is applied Two variables are confounded if their effects on the response variable can be distinguished An experiment in which experimental units are randomly assigned to treatments is called a completely randomized experiment ANS D REF Section 13 AP Which of the following best summarizes nonresponse bias a tendency for samples to differ from the corresponding population as a result of systematic exclusion of some part of the population a tendency for samples to differ from the corresponding population because data are not obtained from all individuals selected for inclusion in the sample a tendency for samples to differ from the corresponding population because the method of observation tends to produce values that differ from the true value a bias on the part of the researcher towards those who chose not to participate in a survey None of these describes nonresponse bias ANS B REF Section 12 AP 449 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 28 A researcher wishes to study the relationship between the level of background noise and mental concentration The treatment noise level will have three levels no noise low intensity noise and high intensity noise the subjects are to be divided into three groups and each group is to receive one of the treatments He has available to him a set of 60 female volunteers and a set of 90 male volunteers What experimental design strategy would help him eliminate the introduction of gender as a confounding variable a strati ed sampling b replication c blocking d systematic sampling e double blind trials ANS C REF Section 13 AP 29 For which of the following types of studies is it impossible to draw cause and effect conclusions 1 Completely randomized experiments ll Randomized block experiments Ill Observational studies a I only b lll only C III only d It is never possible to draw cause and effect conclusions e It is always possible to draw cause and effect conclusions ANS C REF Section 14 AP 30 To estimate the proportion of students who plan to purchase tickets to an upcoming school fundraiser a high school decides to sample 100 students as they register for the spring semester There are 2000 students at the school Which of the following sampling plans would result in a simple random sample Number the students from 1 to 2000 and then use random numbers to select 100 students Survey the first 100 students to register Randomly select 100 students from a list ofthe 950 female students at the school Divide the students into early registrants the first 1000 to register and late registrants the last 1000 to register Use random numbers to identify 50 ofthe early registrants and 50 of the late registrants to survey Select one ofthe rst 20 students to register using a random number table and then select every 20th student to register thereafter ANS A REF Section 12 AP 999 F 450 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part SHORT ANSWER 31 We have distinguished two types of studies observational and experimental Brie y explain the essential differences between these two types of study ANS In an experiment researchers observe how a response variable behaves when they manipulate one or more factors However in an observational study the researchers do not manipulate any factors Instead they observe characteristics of a subset of the members of one or more existing populations REF Section 11 AP 32 The following paragraph describes an actual study After reading the description determine whether the study is an observational study or an experiment Justify your answer with specific references to the information in the study HWe compared paired daytime and night counts of wild brook trout brown trout and rainbow trout made by the same snorkelers in five streams during August 1994 Overall we counted 109 trout in the daytime and 333 trout at night We speculate that trout counted at night were present during the daytime but were hidden from view Biologists should consider that trout behavior and susceptibility to being seen might vary a great deal between daytime and night even during summer In some streams the majority of trout may not be seen during the daytime ANS This study is an observational study since the explanatory variable was not manipulated by the researchers and the subjects were not randomly assigned to different treatments Instead the researchers simply observed the number of trout visible during the day and during the evening REF Section 11 AP 33 The following paragraph describes an actual study After reading the description determine whether the study is an observational or experimental study Justify your answer with speci c references to the information in the study HBefore the opening of the new International Airport and the termination of the old airport children near both sites were recruited into aircraft noise groups aircraft noise at present or pending and control groups with no aircraft noise and closely matched for socio economic status A total of 326 children mean age 104 years took part in three data collection waves one before and two after the switch over of the airports After the switch to the new airport long term memory and reading were found to be impaired in the noise group at the new airport an improved in the formerly noise exposed group at the old airport ANS This is an observational study The children were identified in place and the manipulation of sound level was not randomly assigned REF Section 1 AP 45 1 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 34 Brie y describe how populations and samples differ ANS A population consists of an entire group about which some information is desired A sample consists of only some part of this group that has been selected for study REF Section 11 AP 35 A friend of yours who is not taking statistics wonders why it is that anyone would choose to take a sample quotObviouslyquot she says Hyou would get better information from a census In a short paragraph explain why it is that statisticians take samples rather than taking a census ANS Although we may get better information from a census it is usually far too costly and time consuming to contact every member of the population A large random sample will be nearly as good for far less cost REF Section 12 AP 36 The most basic sampling method studied in statistics is the simple random sample SRS In your own words what is the correct de nition of a simple random sample of size n ANS A simple random sample of size n is a sample that is selected from a population in a way that ensures that every different possible sample of the desired size has the same chance of being selected Note It is important that students not only state that each person has the same chance of being chosen but also each possible sample ofsize n has the same chance of being chosen REF Section 12 AP 452 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part along a mucus hxghway x5 dugammed below r11 Route 55 Buudmg A me duecuens easy to renew he elem m use aemaucsamphng a b ANS a Smce mere are 42 umLs m me pepulauen and we want a sample emze 11gt we want to from 1 m 4 Thengt we would keep addmg 4 m um numberunul we gene me end erme hotel room For examplegt xfwe come upon the number 2 rstgt we weuldsuwey me am momgt me 7LhmomgtLhe numemgt em b n M a a m m a m m along me fvur rows ofmoms REF Semen 1 ZAP 38 Bias is a serious problem that sometimes arises when one takes a sample a In a few sentences explain generally what bias is b What is the distinction between response bias and non response bias a Bias is the tendency for a sample to differ from the corresponding population in some systematic way b Non response bias occurs when responses are not actually obtained from all individuals selected for the sample With response bias however responses are obtained from the subjects but the method of observation tends to produce values that systematically differ from the true population value in some way REF Section 12 AP 39 Bias the tendency for samples to differ from the corresponding population in some systematic way might be due to a selection bias b response bias andor c nonresponse bias In a few sentences discuss the differences among these different biases ANS Selection bias occurs when some part of the population is systematically excluded from the sample Non response bias occurs when responses are not actually obtained from all individuals who were selected for the sample With response bias however responses are obtained from the subjects but the method of observation tends to produce values that systematically differ from the true population value in some way REF Section 12 AP 40 The two paragraphs below discuss aspects oftwo studies each of which exhibit a bias For each study decide whether the problem is selection bias response bias or nonresponse bias and in a few sentences explain why you chose your answer One part of the Nurses39 Health Study is concerned with possible causes of skin cancer Nurses were asked about different behaviors and aspects of their health when they entered the study Then the nurses were given the questionnaire again if they were diagnosed with cancer When the questionnaires were analyzed the investigators discovered that after the nurses were diagnosed with cancer they tended to report a reduced ability to tan It is thought that the shift in reporting might be caused by an awareness of their diagnosis a V b V One part of the Demographic and Health Surveys Program is concerned with measures of malnutrition Investigators measure physical aspects of growing children and attempt to document the physical characteristics of a population at different ages Sadly in some countries many children die early and thus a bias is introduced in the study when the investigators cannot collect the data from the deceased children 454 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part ANS a This is an example of response bias since the awareness of their diagnosis may have caused them to change their response It isn39t non response bias since they were able to obtain responses from the nurses and it isn39t selection bias since they did not attempt to generalize to a larger population b This is an example of non response bias since some of the children selected for the study were not able to participate after they died It is not selection bias since the children were not left out on purpose and it isn39t response bias since the researchers were unable to obtain responses in the rst place REF Section 12 AP 41 Three methods for random sampling are a simple random sampling b strati ed random sampling and c cluster sampling In a few sentences discuss the similarities and differences among these sampling methods Speci cally what sampling circumstances would lead you to choose each of these methods ANS In simple random sampling every individual and every possible sample of size n has an equal chance of being selected for the study In strati ed random sampling the population is divided into non overlapping homogeneous groups called strata and a simple random sample is selected from each strata ln cluster sampling the population is divided into non overlapping preferably heterogeneous groups called clusters and then a random sample of clusters is selected and every member of the selected clusters is studied Cluster sampling works best when the population is already divided into easily identifiable groups that are heterogeneous ie each cluster can reasonably be assumed to be representative of the entire population Strati ed random sampling works best when there are easily identi ed groups in the population that are anticipated to have very different responses to the question of interest Simple random sampling is best when neither of the circumstances listed above are present REF Section 12 AP 42 A pharmaceutical company wants to test its new drug that is designed to help balding men grow more hair From their records of past customers the company has data on about 5000 men The data contains information about the men39s hair color age and percent of baldness A partial list is given below For their anticipated experiment they want to take a sample that is representative of their customers Hair color Age yrs Baldness Light 67 Dark 62 73 Light 41 25 Dark 52 50 Dark 43 14 Light 69 96 Dark 56 57 Light 32 40 455 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part a Brie y describe how you would select a simple random sample of size n 20 from this list of customers b Describe in a short paragraph why you might wish to use a strati ed random sample ANS a To select a simple random sample of size 20 we could number the subjects from 0001 5000 and use a random digit table On the table we would look at sets of4 digits until 20 numbers from 0001 5000 were selected ignoring any repeats and these would be the men selected b If the researchers anticipate an association between any of the variables listed hair color age or baldness and the response variable they should stratify by that variable so that the sample they get will not over or under represent a subgroup which may respond differently than the population in general REF Section 12 AP 43 In evaluating an experiment how would you determine if avariable is an explanatory variable or an extraneous variable ANS In an experiment the explanatory variable is the one that researchers manipulate in order to observe changes in the response variable An extraneous variable is any other variable which is thought to affect the response variable but is not of interest in the study REF Section 13 AP 44 In evaluating an experiment how would you determine if a variable is an explanatory variable or a response variable ANS In an experiment an explanatory variable is one whose value is manipulated or determined by the experimenter while a response variable is one whose value is measured at the end of the experiment REF Section 13 AP 456 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 45 One of the tasks of wildlife biologists is to estimate bird populations One method for doing this is to walk a quottransectquot typically a long randomly selected rectangle and count the number of particular species that are seen During hunting season the biologists wear brightly colored clothes as a protective measure A theory known as the quotspecies confidence hypothesisquot predicts that birds may react to these brightly colored clothes A robin for example when confronted with a biologist wearing an orange color may be less afraid than if the biologist were wearing a brown color The idea is that the orange color gives the robin some quotconfidencequot that the biologist is another really big bird This is a dif culty because a robin that is less afraid of the biologist may be easier to see and therefore quotcountquot because the robin lets the biologist get closer This would result in too high an estimate of the robin population To test this theory a biologist performed a study in her area wearing a bright orange vest or a brown vest while working After training herself to accurately estimate distances she indicated on her notes how close the robins would let her get before they ew away the quotapproach distancequot using this as a measure oftheir quotconfldencequot She randomly selected her starting points in each trip through the transects and also carefully noted the weather conditions speci cally the wind speed a What is the explanatory variable factor for this experiment b What is the response variable for this experiment c After completing the study the biologist was examining her results and noticed that on those days she wore the brightly colored vest the wind tended to be of greater velocity How does this information affect the interpretation of the results of the experiment ANS a The explanatory variable is the coloration of the vest bright vs drab b The response variable is the quotapproach distancequot c The wind velocity is a potential confounding variable On a windy day the birds may not detect the researcher as easily or they may be more hesitant to y Thus it might be that the results are at least partly the result of wind velocity not the choice of garment color REF Section 13 AP 46 The likelihood that an animal will successfully avoid a predator39s attack should increase if the presence of the predator is detected Animals are of course known to warn others of a predator39s presence the well known prairie dog warning call is an example Some aquatic animals are known to send chemical signals For example the crayfish and Iowa darter may excrete ammonium from their gills or possibly in their urine during periods of heightened metabolic activity In an experiment to see if red legged frogs Rana aurora may send or respond to chemical signals specimens in Oregon were collected as embryos and raised in an aquarium As tadpoles they were separated into two pairs of aquaria The quotupper tankquot in each pair was connected to the quotlower tankquot to create a very small river A wooden heron model was placed in one of the upper tanks and moved around for 30 seconds to simulate apredator attack Both the sender upper tank and receiver lower tank animals were monitored for added activity increased movement indicating antipredator behavior a What is the explanatory variable factor for this experiment b What is the response variable for this experiment 457 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part A O V During the course of the experiment the investigators were very careful with the wooden heron model not to come in contact with the glass of the aquaria or make noise in any other way If they had been unsuccessful and their wooden heron made significant amounts of noise how would that affect the interpretation of the results ANS a The explanatory variable is the presenceabsence of the wooden heron model b The response variable is the antipredator behavior c The added noise would be a potential confounding variable The tadpoles39 response may be a startle response to a sudden change in their environment and not specific to the detection of a predator PTS 1 REF Section 13 AP MSC Section 13 47 A common practice of teachers is to have students exchange their quizzes and grade each others In addition to decreasing the teacher39s work load the reduced time between quiz and feedback is thought to be a plus for learning Your US History teacher aware of your statistical prowess has asked you to design an experiment to test this theory You have decided to use the mid term exam not graded by students as your response measure Your history teacher has three classes one early in the morning one at noon and one late in the afternoon Each class contains 30 students a Describe the treatments you will use in your experiment b One possible confounding variable is the time of day since students may be more alert at certain times of the day than at other times Describe a method would you use to control this variable Unfortunately you cannot change the student schedules c Do you feel the results of your experiment could be generalized to your statistics class Why or why not ANS a Individual pairs of students would be randomly assigned to Htrade papers or Hrlot trade papers treatment groups The non trading students39 work would be graded by the teacher each day and given back the next day b Each class would be considered a block Within each block both treatments would be randomly assigned as indicated in part a c The results might be generalizable to other classes but wo doing the experiment in those classes there is no evidence suggest one could generalize Statistics and history seem like they might be different enough that although they are both classes with homework the subject matter might be learned differently and the instant checking of the quizzes might be less or more ofa help in one class or the other REF Section 13 AP 458 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 48 In competitive sports video recorders have been used more frequently in recent years The idea behind the recorder is that coaches can replay training sessions for more effective feedback to the athlete Some people believe video recording may make the athletes more nervous and actually decrease their performance You have been asked to design an experiment to address this issue for competitive high school tennis players You have decided to use the accuracy of tennis serves as your response variable and the number of successful serves out of 100 as your performance measure The subjects for your experiment are 60 high school male competitive tennis players of varying ability who have volunteered for the experiment a Describe the treatments in your experiment b One possible confounding variable is the experience levels of the players Explain how you would control this variable c Can the results of this experiment be generalized to all male tennis players Why or why not ANS a The two treatments will be 1 The subject is recorded and 2 The subject is not recorded b lwould use blocking pairing to control the experience level of players I would pair the two most experienced together as one block the next two most experienced as the next block and so on Then the two members of each block would be randomly split into the two treatment groups This way each treatment group should be roughly the equivalent with regard to experience level c No the results of this study should not be generalized to all male tennis players for at least two reasons One competitive tennis players are presumably more used to playing in front of crowds and would be less bothered by video recording than the typical player Two volunteers are not generally representative of any larger population Note either reason should be suf cient to receive credit REF Section 13 AP 49 Suppose that two experiments were conducted to assess the effect of a new insect repellant In Experiment A a simple random sample was taken from the population of River City In Experiment B a simple random sample from a group of volunteers from the population of River City was used The results of the experiments were the same fewer insects landed on the arms that had been treated with the insect repellant The volunteers were randomly assigned to the two treatments in both experiments a For each experiment A and B discuss whether one can legitimately infer a cause and effect relation between the use of the repellant and fewer insects landing from each of these experiments Why or why not b V For each experiment A and B discuss whether one can legitimately generalize to the population of River City from each of these experiments Why or why not 459 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part ANS a In each of these experiments we can infer a cause and effect relationship because the volunteers were randomly assigned to the two treatments b In experiment A we can generalize the results of the experiment to the population of River City since the subjects were randomly selected from the population of River City Thus the subjects should be representative of the population in general However in experiment B the random sample came from a group of volunteers from River City who may not be representative of the general population of River City REF Section 14 AP 50 Suppose that two experiments were conducted to compare the effects of two new insect repellants In Experiment X a simple random sample was taken from the population of River City and the citizens were randomly assigned to repellant A and repellant B In Experiment Y a strati ed random sample was taken from the population of River City and the citizens were randomly assigned to repellantA and repellant B River City has 4 geographic areas of town the NE NW SE and SW quadrants 100 people from each quadrant were sampled for Experiment B The results of the experiments were the same fewer insects landed on the arms that had been treated with insect repellant A a For each experiment X and Y discuss whether one can legitimately infer from each of these experiments that repellant A is better than B Why or why not b For each experiment X and Y discuss whether one can legitimately generalize to the population of River City from each of these experiments Why or why not ANS a In each of these experiments we can infer a cause and effect relationship because the volunteers were randomly assigned to the two treatments b In each of these experiments we can generalize the results of the experiment to the population of River City since the subjects were randomly selected from the population of River City Thus the subjects should be representative of the population in general REF Section 14 AP 460 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part Chapter 02 Graphical Methods for Describing Data Distributions TRUEFALSE l A data set is discrete if the possible values are isolated points on the number line ANS T REF Section 2 AP 2 A data set consisting ofmany observations ofa single characteristic is a categorical data set ANS F REF Section 2 AP 3 A data set is multivariate ifit consists only of numeric variables ANS F REF Section 21 AP 4 Frequency distributions can only be used with categorical data ANS F REF Section 22 AP 5 The relative frequency for a particular category is the number of times the category appears in the data ANS F REF Section 22 AP 6 Bar charts should be used with categorical data ANS T REF Section 22 AP 7 Dotplots work best for small and moderate sized numerical data sets ANS T REF Section 23 AP 8 An outlier is an unusually small or large data value ANS T REF Section 23 AP 9 The quantity W often gives a rough estimate of the appropriate number of intervals in a histogram ANS T REF Section 23 AP 10 A curve with tails that decline more rapidly than the tails ofa normal curve is called a heavy tailed distribution ANS F REF Section 23 AP 461 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part ll The density ofa class can be calculated by multiplying the relative frequency of the class times the class width ANS F REF Section 23 AP N For stem and leaf plots with single digit leaves commas must be used to separate the leaves ANS F REF Section 23 AP 13 One advantage of histograms is that they may be used for large data sets ANS T REF Section 23 AP 14 If the upper tail of a distribution stretches out farther than the lower tail the distribution is negatively skewed ANS F REF Section 23 AP 15 In a scatter plot both the horizontal and vertical axes must be set at zero ANS F REF Section 24 AP 16 A pie chart is most useful for numeric data ANS F REF Section 25 AP MULTIPLE CHOICE 17 A survey form solicited the following responses 1 age of respondent ll gender of respondent ImtlevelofJOb 1 iii a 11 1 1 a 11 a i1 satisfiedcompletely satisfied IV annual income Which of the responses represent categorical data a I only b H only C III only d H and Ill only e All the responses are categorical ANS D REF Section 2 AP 462 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 18 The following relative frequency distribution summarizes student responses to the question If you could make your college choice over would you still choose to enroll at your current college Which ofthe following is the correct bar chart for the response data a d 05 045 Kelmivefrequency Relativelrequency Denmt iv thablv gtrahamvna minivan Defuwelv mum Prohzblwm aenmw v25 v25 no yes V25 rm Respans Kiwanis Relativelrequency Relativelrequenzv De nitely Pmbahly Prahablyna De nil lv nemvei Prababh ambamwm De nitely yes yes rm ms v25 rm Respnns RESDonse Rzlmivefrequency Definim l Prnhably Wabalzlyna De nitely YES v25 Ha Respanse ANS E REF Section 22 AP 463 2014 Cengage Leaming All Rights Reserved 39 duplicated u 39 39 39 39 L 19 Which of the following variables are discrete l the volume ofliquid in a l6ounce bottle of soda pop H the percentage ofmales 1825 who actively view online pornography III the number ofbroken eggs in a paclcage ofa dozen eggs IV a count of the statistics majors at a certain university a H only b H and Ill only C III and IV only d I only e All of these variables are discrete ANS C REF Section 21 AP 20 A survey asked adult respondents how dependent they were on various electronic devices The accompanying table summarizes the responses without Select a comparative bar chart that shows the distributions of responses for the three different technologies a d lEaHna39m39Eng m m Rclulivc l39I39cqulncy Relmwc I39I39cquclwy mmaaeme w mm arsenal cell a Dersanal Cell v Cmvnutsr Phanz iier Can nuter lene 2 464 2014 Cengage Learning All Rights Reserved 39 duplicated u 39 39 39 39 L 39 lEannazmtigme V liannoumagmz hvmgwwham vangham lWauidmss m auidmss m cumin nu Wm amid da mm Al auiudenmteivhve a avid defuwzi hve whw V L mm Peysanai EH m Persnnai LEH uvn immune Phane Wager Carvpuzer pm Never c PEYSDHB EH DVD ANS B REF Section 22 AP 21 According to the stemandleaf display below hoW many times does the number 58 appear in the data set Slom Thus Lvnf Hum 5 l 39l 2 2 F1 8 SFJ D 131181 7 ii1 8 1H DCLOU DD U IU th O oo ANS C REF Section 23 AP 465 2014 Cengage Learning All Rights Reserved 39 duplicated u 39 39 39 39 L 39 12 thch othe followmg Stan and leafplots corresponds a data dismbuuon that 15 posmvely nght skewed7 110539 I and m ohty None onhe dismbuuons 15 posmvely skewed ANS B REF Secuonl 2 AP 23 community are summanzed h the hhstogam below m u 24 w m m m we m thmx lnwnu Umummdw hr du ud Ha no What propomoh of households have annual mcomes 911000 ormore7 macaw ANS D REF Semen 2 4 AP 24 communlty are summanzed m me hlstogam below W l l l l l l l gt loll g ll a me i we zue o W 2a lo 0 an N m M a m m 2 Allmml hllaulu l39llmumlub lll mums a moo b osoooo c oaoooo d o7ogtooo o2oooo SecllonZZAP ANS c REF 2s enrolled m publlc lnstllullons for me so U 5 states What 15 me relauve frequency mule 7o m lt Bonner317 e 5o ANS c REF Semen 2 2 AP 25 The cumulatwe relatwe frequency plot shown was cons ta on the percentag of college students enmued m pubhc rnstrtutmns rerthe 50 U 5 states Whmh of the onewrng is closest to the apprexunate ptdpdtttdn of states that have more than 90 percent of college students enrolled m pubhc rnstrtutrensv Cumulume Maxim frzquznry 40 5A an m Rn gu mu Pzrccmuge emcued macaw ANS B REF Secuonl 2 AP SHORT ANSWER 27 were gwm 5gt 10gt or 15 extra credrtpmnts dependmg on therr1eve1 ofpamcxpauon m the expenrnent t am A Fr h h A t h m t 15 dtscrete or wnunuous a The true lmgvh of the path b The amount of credrt gwen to the volunteers c The lengvh othe path as Judged by the students d The number of 90 degee turns e Class standrng Numerical continuous Numerical discrete Numerical continuous Numerical discrete Categorical REF Section 21 AP 28 In a study of how college students give directions from maps 40 lntroductory Psychology volunteers 20 men and 20 women were given the task of giving directions to another Observations were made of subj ects direction giving behavior in the experiment a b C d 6 whether the map was available or the directions were given from memory the sex of the direction giver the distances given as part of the directions the number of times directions such as North Southwest etc were used and the frequency of errors in the directions For each of the variables in this experiment determine whether it is categorical or numerical For each numerical variable determine whether itis discrete or continuous a whether the map was available or the directions were given from memory b the sex of the direction giver c the distances given as part of the directions d the number of times directions such as North Southwest etc were used e Frequency of errors in the directions ANS a Categorical b Categorical c Numerical continuous d Numerical discrete e Numerical discrete REF Section 2 AP 469 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 29 Statesgt the percentage oflndlvlduals ln that age goup who are reglstereclto vote voung m me 2000 Elecuons u Vo REElsteved v mm 1572 25m 6553 5577 75 u out a Descnbe ln a few sentences the regrstratron pattern that you see ln the clata above 3 ln your oprnrongt would that explaln the regrstratron level for the 18 e 24 agegoupv Why or why notv ANS a The proportron of people reglsterrng 15 smallest for the 18724 yearrold goupgt and gets larger wth agegt untrl hnally decllnlng ln the 75 yearrold goup b m M l REF SectlonZZAP 20 lt ll h l t h t nests m and 15 clay pornts of the experrrnent Cumula w count orasprsaatsa Egg Orlglnaln I ma Scheok I ma lOoheck I Ba 15 check I 27 12 17 19 27 z 12 18 42 7 22 44 47m 1mm 157day check amfmal nests m the gm Do not wnven39he table to a gaph Eggs Prednted Natural nests my mum way check may check may check b D2 Scheck Dz lOcheok Dz 15mm REF Semen 2 2 AP 31 Birdrplane wlhsmus mvolved specie a Ccns39mct a bar chart to display me bird spemes data for me land 13g runway b takeoff runway ANS 3 landingRunway llisions Zebu am Mmmkm in Have gamma spun b REF Semen 2 2 AP MSC Semen 2 2 Iowa mes a me dmerem muss yourbar char fm39pan a ANS a Child Restraint Compliance 11 d E 5 an d 1 6D E L 4n 2 n 2n HP CR G c M mryonown b Cedar Raprdsgt and Iowa any have hxgher oornphance rates than Guuenberg and Manchester REF Searon 2 2 AP 32 quesuons 1 Do you Lhmk me Unned States should let Communist newspaper reponers corne m here and send back to that papers me news wunmes as they see u fr orn other 7 wme m and send back to Arnenca the news as they see rm asked these quesuons m dxfferml orders Rupnmax tn quotpanquot qnzx nnin 194s a Ccns39ructa wmparahvebarchan for these response percentages b d1fference 1n the responses7 Explam ANS a wmparauve bar chart Q1 Frrst Q1 Secund Quesuun order L The rate of questron was asked anertne one about Arnencan reporters 1n Russra REF Semen 2 2 AP 24 Bro1ogrsts know that bats have d1fferent 1ghtcharaaensucs Sorne bats exnrbrt fastgt strargntgt and long argnts others are rnoderate1y s1owgt and nrguy maneuverame The mm a m t 1aws ofphysms The data presented below are wmg wergnts 1n garns for oertarn spemes ofbaLs a msewealers Frurteaters 99gt 115 t711595gt 122121129gt 15 ogt154gt1z 122 411114 zgt1054gt20 9 1nsecteaters 2221151142gt29gt75gt25129 a wergnts for the two categones onsatsgt frurteaters and msecleealers about the d1fferenoes 1n wmg wergnt for mute and mseaeealer ANS a Frult Eaters wlng werght 5m 75 Wlng Welghl lnsea Eaters wlng welght 5m 75 Wlng Welghl bats They ar 0 uoh more spre lusecleeallng bats only have a range a REF Sectlonz 2 AP acl out lnwelgntranglng from 9 9th 114 2 grams The r 5 to 22 2 grams Exhibit 271 years ofteaohlng expenmce for the elementary schools ln Des Mornesgt Iowa The clatagt by elementary school appears ln the table below Yms Yms ms ms SChmI Exnn SChmI Exnn SChmI Exnn SChmI Exnn darn 13 x llanawalt lz7 cKee l7 5 bully lo 5 apxtul Vlew 9 7 Hl ls l7 cKmJey 5 a leasant Hm l2 2 ausll x 5 llnw 14 9 che a z vex Wands 5 9 Dung 13 x Hubbeu l5 l nnme 162 tnwe 16 5 anntawn 7 o anksnn 16 x nnre 16 a tunebalrer IR A Edmund x 4 effexsnn l9 2 nrns 9 9 allase 4 x Fmdley 14 9 Km 7 o nnlt x a mam 9 7 artnn 9 Lungfelluw 9 2 a1 Park ll 4 mdsm l7 7 r l7 2 Luvejuy 9 9 ark Avenue ll 4 andhwn l7 eenwnnn 14 adxsun 20 x erlnm ll ngnt l2 9 5 Refer to Exhxbn 271 a Ccns39mct a hmogam for these data usmg me followmg class intervals 0 m lt 4 5 m lt 2 etc any unusual features ANS a gt 14 m 5 2 w w w w u 4 1 1 2U 24 We rsEx amen e 5 skewed toward me hxghervaluas REF Secuonl 2 AP Exhibit 272 Iowa The datagt by elemmtary schoolgt appears m me table below 5 Refer to Exhxbn 271 Cuhsuua a hhslogam for mese chmgt usmg me followmg class rmervsxs o m lt 20 20 m lt 40gt em b Descrrhe the drsvrrhuueh ofFreeReduced ehgxbxmy peroehcsgt and note any unusual features ANS 3 15 m 5 n 2 6D 2 mn Free Reduced n m h r drsmbuuoh REF Secuonl 2 AP 27 a m hum exphrh Lhexr food selemon The Amalum of an morser arcade 15 a measure of ms shapegt m m The browsers and gazers mlhe rummm famny Curvature Browsers vs Grazers Browsers Grazers N 18 N 54 1 1L 1 1 1H 1 9 1 2L 1 1 4 1 3L 1 22244 99885 1 3H 155566667778999999 4101 4L 1022223 99987 1 4H 155556666677778889 321 1 5L 1 03 1 5H 1 9 1 6L 1 0 1 6H 1 1 7L 1 0 1 7H 1 a Brie y describe each of the two curvature distributions browsers and grazers noting any unusual features of the data b The theory of some biologists is that browsers have thinner mouths because the browse plants frequently have thorns and spines browsers have evolved to have thinner mouths to get beyond the thorns and spines to the food part of the plant Is the data in the back to back stem plot consistent with this theory What aspect of the data would you consider when answering this question ANS a The distribution of browsers is centered in the low 40 range Other than one prominent outlier at 70 the distribution is approximately symmetrical The distribution of browsers is likewise centered in the low 40 range and is quite symmetrical but more spread out than the browsers if the outlier is excluded b The evidence to support this theory is not very strong The browsers may have a slightly higher average curvature but the two distributions overlap quite a lot indicating that the differences are modest at best REF Section 23 AP 38 An experiment was performed to determine which brand of comparably priced light bulbs A or B lasts longer on average Ten bulbs of each brand were tested and their lifetimes recorded in hours The data are shown below a b V Bulb A 88 97 110 122 128 129 135 141 150 165 Bulb B235593106111115123128153171 Display these data using a comparative back to back stemplot What are the differences and similarities in the lifetime distributions for the two samples 478 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part C ANS If your preference for brand A or B must be determined from the information in parts a and b which brand would you buy Explain your choice using appropriate statistical terminology a Stemplot Bulb A vs Bulb B c Bulb A hrs Bulb B hrs 17 l 5 16 0 15 3 1 l4 5 13 Stem tens 9 8 2 12 3 8 Leaf ones 0 ll 1 5 10 6 7 9 3 8 8 7 6 5 4 3 2 3 l 0 The two distributions are similar in being reasonably symmetric The distribution for Bulb A is less widely spread out and the values are generally a little higher than for Bulb B I would buy Bulb A since the center of the distribution is higher and the variability is lower so I think I could count on getting a quality bulb with A more so than with B REF Section 23 AP 39 The stem plot below displays the weights in ounces ofa random sample of tomatoes grown on a local farm Weights 0f Tomatoes oz 2Ll 4 ZHl 3Ll 2 3Hl 89 4Ll 13 4Hl 5589 5Ll 11122334 5Hl 668999 6Ll 223344 6Hl 5556 stem ones leaf tenths 479 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part a Enemy destrrbe the drstrrbutroh oftomato wergrts b What 15 the werght of the heavrest tomato h the sample7 ANS 3 the hxgherS categorres and fewer m the lowerS wergqt categorres b The heavrest tomato 15 5 5 ounces REF Sectroh 2 2 AP 40 Eat charaaensucs and Costa cha Two categorres orbat spetres are represented fruxlreaters and msearealers Frurt eaters 2s2gt272gt42 0A4 231232212 Q18 1301270 1gt41 552452 152 9 hsett eaters 222gt274gt210gt22 9gt275gt224gt12 7 a spans for the two categorres orbats fruxtrealers and mseclrealers about the drrrerehoes rh wmg span for front and mseclrealer ANS a Frurt Eaters whgspah used Eaters Wingspan u on vvmgspan b masters are generally longermm crude msecteeatlng bals The e wlngspans for u wlng5pan5 are also more spread eul for me fruueealersgt from 25 2 lo 52 7 cmgt compared lo 12 7 lo 22 2 crude msecleealers REF Sectlonl 2 AP Exhibit 24 In the aruclegt Scallng ofMammallan Long Bones Small and Large Mammals Compared the r a l h r a n V specles l ems leveliceshmm ran erermeslmnn esu em E m E ran a a rm ezu em u 5 mu an 2mm 25m arm n 5n mu 15D 2mm 25m 3mm s u 5 luu 15D 2m 25m auu 4l Refer to Emma ANS skewed The humerus and femur exlmd a lmle hlgher39han me ulnagt to about 300 vs 200 REF Sectlonl 2 AP 42 Refer to Exhibit 2 4 Biologists speculate that the different amounts of weight might be supported by different sized bones Based on the histograms does it seem like one of these bones has on average a greater or lesser circumferences Explain ANS The differences are not great since the large parts of the distributions are very similar Perhaps for the largest animals the humerus and femur support more of the weight indicated by the fact that these distributions extend to higher values than does the tibia distribution REF Section 23 AP 43 In birds the muscles that pull the wing down and thus cause the actual ight are the Hlarge pectorals In the article HDimensional Relationships for Flying Animals the author reports the following pectoral muscle weight in grams for birds of prey Rapaces diurnes voiliers 958 715 299 476 223 270 194 226 1135 798 149 842 738 538 36 48 151 a Construct a stem and leaf plot of these data b In a few sentences describe the distribution of the pectoral muscle weights ANS a stem and leaf Pectoral muscle weights grams 5 8 stem hundred 15 leaf ones 76 23267099 13495194 9 8 7 6 5 4 3 2 1 0 364854748o84 b This is a skewed distribution with most weights under 200 grams but extending up almost to 1000 grams The highest values are extreme outliers REF Section 23 AP 482 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 44 In the article HDimensional Relationships for Flying Animals the wing areas in square centimeters of gliding birds of prey are reported Night hunters are distinguished from the birds that hunt during the daylight hours and the wing areas for samples of each type of bird are displayed in the following table Wing area of gliding birds of prey sq cm Night hunters 3715 1082 1396 405 1163 1304 459 Day hunters 1317 822 530 2321 708 703 1285 558 438 a Construct a comparative back to back stem amp leaf plot for the wing area for the two types ofbirds b Biologists speculate that since birds could be detected at a distance by their prey during the day the species that hunt during the day should be smaller on average than those that hunt at night Are the data as displayed in part a consistent with this theory What speci c aspects of the plot in part a support your answer ANS a Back to back stem and leaf Day hunter wings cmz Night hunter wings cmz stem thousands 3H 715 leaf units 3L 2H 321 2L 1H 317285 1L 082163304396 822708703558530 OH 438 0L 405459 b Yes the majority of day hunters are below 1000 cm2 while for night hunters the majority are above 1000 cm2 REF Section 23 AP 483 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part below displays me distribution ofongen wncmu39auons along me Cedar Rwer Cumulmive nequen 39Distriluniuu mgl Niungeu Cedar Rwel 39 39 MA 1 a 5 u a u 1 5 3 rr more7 c 50 otheNmegen wnoenu39auon measuremean he below what approximate value7 ANS 3 Approximately 20 b Approximately 10 c 5 e 5 5 mg L REF Secuonl 2 AP below displays me distribution ofongen wncmu39auons along me Skunk Rwer Clunulmivv freqlwluy Dimmum Ing L Nitrn n Skunk R er a mEJm b quotKiev 0 50 ohm ngen wnoenu39auon measuremean he below what approxxmate value7 ANS 3 Approximately 75 b Approximately 20 c 5 mg L REF Secuonl 2 AP 47 N nh n m eml Length mm mi em a Descrrbe m appropriate scausmal terms me drsmbuuehs oftheselwo vanahles The drsvrrbuueh ofhead lmg39hs oenarhly appears to be ramersuahge What do you Lhmk mxghl acwunt for me shape enhrs dismbulmm fromOto mm enwesubpepulauehs mm 15 case perhaps males are larger ersrhauergt or mere may be two subspecres of sh that make up me rdehmred specres REF Secuonl 2 AP Exhibit 23 There has been a recent increase in the popularity of caffeine containing Henergy drinks or Hfunctional beverages substances that are considered to be food that may provide some health bene t However caffeine in these drinks presents an important health concern especially for women of childbearing age Studies have shown an increased risk of spontaneous abortion and low birth weight children to women consuming more than 150 mgday ofcaffeine In a recent study eighteen 12 02 servings of different brands of carbonated sodas were analyzed to ascertain their caffeine content with the results presented below The data are in mgl 2 oz serving if no caffeine was detected this is reported as mgserving Caffeine mg in 12 oz servings of Carbonated Sodas 295 382 396 295 317 274 454 482 360 338 194 180 346 48 Refer to Exhibit 2 3 a Construct a stem and leaf plot of the caffeine content for the detected amounts of caffeine b In a few sentences describe the distribution of the caffeine content How would your description change if the Hnone detected were treated as 00 mgserving ANS a stem and leaf Caffeine mg 1 l 1 1 8094 2 l Stem tens 2 l 749595 Leaf units 31 173846 3 l 608296 4 l 4 l 5482 b This distribution is fairly uniformly distributed with small gaps near each end REF Section 23 AP 49 Refer to Exhibit 2 3 a Construct a comparative back to back stem amp leaf plot for the container vs fountain amounts of caffeine Do not use the data for carbonated sodas where caffeine was not detected Describe how the two distributions compare b What do you think might explain the differences between the two distributions 487 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part ANS a Back to back stem and leaf Fountain Container l 1 l l 1 lso94 l 2 l l 2 l749595 Stem tens 413026111107l 3 l173846 Leafunits 636352l 3 l608296 4 4 l l l l 5482 b There does not appear to be an appreciable difference in location The difference in variability perhaps indicates a difference in quality control over the fountain syrup process than the container process Perhaps there are more steps in the container process or perhaps the raw materials are more variable in the container process REF Section 23 AP 50 Artificial bird nests have been used extensively when studying predator behavior The assumption is that predators will find and respond to artificial nests in the same way they do to the natural nests In a study to test this hypothesis the predation of 27 American Robin T urdus migratorius nests and 27 artificial wicker basket nests were compared Artificial nests were placed 30m from existing robin39s nests in a randomly chosen direction The natural nests and arti cial nests were checked at 5 day intervals and the number of nests out of 27 that had been disturbed by predators in the interval was noted The results are as follows Numbers of real and arti cial Robin nests predated 5 day 10day 15day Nest type check check check Natural 12 l7 l9 Arti cial 3 12 18 a Construct a time series plot for the number of natural nests disturbed by predators Use the same set of axes to plot the number of artificial nests disturbed by predators b Does it appear that the artificial and natural nests have the same pattern of predation Justify your answer by appealing to specific aspects of your plot in part a 488 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part b h On An hA Lhanaturalnesvs REF SecuonuAP 51 Records othe rnrssrons onst Cantornu m me form ofbapusms and bunal records provrde sn rdesl opportunny to examme me consequences ofwhat 15 lcnown as me Colombmn I hang gt bspusrns at two Cams 5st rnrssronsgt San Jose de Cornondu and San Genrudrs The data are for me decade 177071 79 Baptisms in the Baja San Jase oe Camandu San Gemums Collin 0 anprisms to me graph mission and what year seems to be the most likely candidate Again justify your response by appealing to the graph ANS a Generally the trends seem to be parallel except for an apparent greater variability at San Gertrudis in the 1770 1773 period The two curves run roughly parallel except for those initial years of the decade b V The most likely candidate is the San Gertrudis mission in 1772 There is a precipitous drop in the number of baptisms in the 17711772 time frame which would be consistent with a population loss due to disease Another possibility is that so many baptisms occurred in 1771 there weren39t many people left over for the 1772 baptisms REF Section 24 AP 52 In a story written in December 2002 the Des Moines Register reported on the percentages of students who qualify for FreeReduced lunch programs in the elementary schools in Des Moines Iowa The data by elementary school appears in the table below School quot0 FR School quot0 FR School quot0 FR School quot0 FR Adams 64 Hanawalt 14 McKee 55 Phillips 27 Capitol View 78 Hillis 35 McKinley 78 Pleasant Hill 17 Cattell 55 Howe 49 Mitchell 64 River Woods 48 Douglas 45 Hubbell 31 Monroe 52 Stowe 56 Downtown 8 Jackson 60 Moore 42 Studebaker 30 Edmunds 83 Jefferson 5 Morris 54 Wallace 80 Findley 64 King 71 Moulton 88 Willard 82 Garton 53 Longfellow 84 Oak Park 59 Windson 37 Granger 52 Lovej oy 66 Park Avenue 38 Woodlawn 40 38 Madison 58 Perkins 54 Wright 29 The data presented in the table about the Des Moines Iowa elementary schools was from an article that related the percent of children eligible for Free and Reduced lunch and teacher experience The percent ofchildren eligible for FreeReduced lunch is generally regarded as an indicator of the socio economic status of a neighborhood The concern of the Des Moines Register in the article was that the least experienced teachers typically teach students from low income families The accompanying scatter plot shows the data from the article 490 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated 01 postedto a publicly accessib1e website in whole or in part YearsEXrI Vs FreeReducede 2m 15 g u m 5 d Zn on an so an an n FveeReduced a rd an App or mm scatter plow b m n r m ANS 3 m experreme should demease b only moderate at best REF Searorr 2 4 AP 52 Invesugalors wnung m the harm manly Addzmence were rmeresced m the commumcauon aboulsex and related topics betwem parmLs and 1214 year olds The h 104 rrgt q q p r drscussed chxldbxnh Thxs would be recorded as the point 57 a 72 4 Pawan Vs Anulesteuts Wyoming of Discllssinn Sec Ellllcmjml Tnpics 1 Vest 9mm 3 1 1 11 12535 as 55 75 55 1 55 511mm 3 On the gaph above sketch the hue yx represmung a ma of perfect agreemmt between the parents and admescehts the hue you sketched 1n pan 37 ANS 3 Draw dxagonal lme mm 1515 at lower le to 9595 at upper nght PTS 1 REF SectmnuAP MSC Semon24 54 such as L1fegtSporLsgtand Cars p t Oppoarte sex as a 5 2gt whde grrta on average rated therr rhtereat rhthra toprc as 5 0 oh the 7 pornt rhtereat scale Thhs 15 recorded as the pornt 5 2gt 5 o n rquot r w a n a s a t 2 a o a 5 hate ha can you rhrer from each ortheae features othe acatterplotv a The pornta generally seem to scatter around the hhegt yr b m t t a m m a the upper rrght onhe gaph 0 What can be aard about the toprca these pornta repreaehtv ANS 3 the avenge rhtereat for toprca 15 about the same for boys and grrta a rhtereatltrhrdd1e cluster and hrgd rhtereat upper nghl cluster 0 VAN h REF Sectroh 2 4 AP b 0 data ANS a 45 students 15 x 200 more than half othe preferred dunks Relauve frequency bar chan Su Drink Prefersm9 mam balmy Coke Peysx 311m DxPewex mm m REF Semen 2 5 AP 56 One of the Hmedia messages sent by television is that appearance is a very important aspect of ones being These messages are thought to spur young women to have unrealistic expectations about beauty thus spending billions of dollars on cosmetics and toiletries Some of these messages were studied during the 1999 2000 prime time television season when investigators kept track of the appearance comments Some of their data comments by males classi ed by gender of recipient and type of appearance comment is reproduced in the table below Insults Compliments and Neutral Appearance Comments Males commenting Males Males Nature of comment about males about females Compliments 52 106 Neutral comments 60 35 Insults 41 15 Totals 15 3 156 a Construct two pie charts one for comments about males one for comments about females to summarize the data above b Using the information in the table above and the pie charts in part a display the given information in a comparative bar chart In the same study of appearance comments mentioned comments by females were tabulated That data appears below Insults Compliments and Neutral Appearance Comments Females commenting Females Females Nature of comment about males about females Compliments 49 Neutral comments 26 57 Insults 21 32 Totals 96 168 c Display these data in a segmented bar chart to compare the distribution of comments in these two samples d Based on the information from the graphs in parts a c how do the distributions differ when men rather than women are making the comments and how do they differ when men rather than women are the recipients of the comments 495 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part NS 3 Compmuve pie charts for commmts about males and males Males abuut males Males abuut females b Compmme bar chm for commmls aboutmales and males Camphment Insuu N 51 Nature afCamments a Cummenls by males mm if on on o m on mm m on Recipient of cummenl d upon me gender othe recxpxml Men makmg commean are much more 11181le be sarne pattern whether the rempxmt 15 male or male drstrrtmtedgt meanmg a male can expea an rnsult about as frequently as a cernphrnent REF Sectren 2 5 AP 57 tt m Jab Sa xfaajnn nrlt 55mm annual inmme me Mnaeratelv Verv x ml D x red sea ma Constanta and sketch a pre chart for these data ANS pre char D Very Drssat I Lrtue Drssat D Moderately Sat D Very Sat PTS 1 REF SemenZSAP MSC SemenZS 52 In recentyears there has been a change m the gocery shoppmg habrts ersheppers nerenanrr AA The stacked N a t t a Convmxmoeslores for 1922 and 2005 Gracely S101 Malkzl sum a 1n a fewsemenoes desmbehew the prepemeha ermarketshare have changed for Lradmonalgocerystores from 1922 to 1005 03 share m 1922 What aspen of the chart shows th157 ANS to 502a Meat ofthhs market share went to the nonru39admomlgmoery scoresgt thh nvemenoe stores gomg mm a mt under 10 to about 15market share 9 for the nonru39admonal stores for the two years appears to be at 1east5 REF Sectmh 2 5 AP 59 table Mnthzr39 pali cal idzn ca nn nfxtndznt Dunncxatx Ind mam mama ma Cohstma and sketch a pie chart farthese data ANS pie chart REF Secuon z 5 AP 60 a l each household The cmsus data for four decades is summanzed below Households by Size solemn Years 1970 in 2mm wmwll amulqu s peonlc w lmrc a mom 1 m0 2 mo from1970to 2000 b Whatslze ofhousehold appears to have decreasedthe mostfrom1970t020007 ANS a The propomon ofhouseholds ml 4 people has demeasedsllghtlyfrom15 5 of households to 14 6 b m h I 1th mallow I m 0 m m slze or only decreased sllghtlyl REF Secuon z 5 AP Chapter 04 Numerllal 39 39 ninrihu TRUEFALSE l The mean 15 the rnlddle value of an ordered data set ANS F REE Sectlon z 2 AP 2 One dlsadyantage ofuslng the mean as a measure of center for a data set 15 that us value is affected by the presence ofeven a smgle outller m the data set ANS T REE Sectlon z 2 AP 2 The vanance 15 the posltlye square root othe standard devlauon ANS F REE Sectlon z 2 AP 4 For any glyen data setgt the rnedlan rnustlae geaterthan or equal to the lower quartllegt and less than or equal to the upper quartlle ANS T REE Sectlon z 2 AP 5 The lnterquartlle range lsreslstant to the effect ofoutllersl ANS T REE Sectlon z 2 AP 5 By clennltlongt an outller is extreme mt 15 more than 2 0 up away from the closest quartlle ANS T REE Sectlon z 4 AP 7 ltthere are no outllersgt a slceletal and modlfled boxplot can dl er m the lengvh othe boxgt but not n the whlslcer lengvhs ANS F REE Sectlon z 4 AP MULTIPLE CHOICE 2 The dot plot below shows the annual saunas In thousands ofdollam ofa sample of nonamanaganmtslaffwho work for a smallbanklng company m maunrula o durum sun salary7 a b mode 0 rnedran d rnterquartrlerange e range ANS c REF SectrenzlAF 9 The table below surnrnarrzes the number errnrnutes spent exerclslng each day for a sample one female college students ll l3 l l ll w ll l u 7 h l m s l 2m l mu la 2 107 x 2 a H a ll 2 gt 2 ean spread standard devratren b c rnterq a nge 0 center rnedran spread standard devratren d c t quanllerange REF Sectlon 2 1 AP crude mean and standard devratlon 45m 494 533 244 392 4U8118 7m SH 565 mm 566 232 353 564 375 4ul zuz 28 24 uunces REF Sectlon z ZAP 11 mama are shown below An 48 n 45 211 78 711 31 511 54 55 45 511 3D n 2n Compute the mean and standard devmuon for the above data set 5 tccnts 7 11 1ccnts 4n 4 cents 2 ts zutcents s 111 1 cents 48 2 cents 17 2 cents ANS E REF Sectmn z zAF 12 Data ent1pp1ng pement forlorastauranttables are an n ADD 3115125114 552 nn 1111 155 4114 2511 277 2891MB 211111111 11111511511 Compute the value ofthe mechan for the above data set a The med1ant1pp1ng percentage 15 10 e 152 The med1ant1pp1ng percentage 15 22 2 ANS c REF SecuonZZAP 12 Data onweekdayexerchsetme 1n mmutes for 20 ma1es areshewn below Ccmpute the mtecquanne range Ma1eWee1ec1ay 545 5 35 an 1111 2751575 SBEI 14115 9D 11111 31111 1111 71111 3115 1111 53111535 an an a b c 5475 d e ANS D REF Sectmn z 2 AF 14 states 1n the wnunmtal Uruted States 77 211 41 a 35 111 1a 135 7D 37 86135 35 53 42 15 28 12 m 32 53 211 25 17 m 32 213 1a 35 211 4111 133 45 5 86 35 7 m 155 33 35 u z 25 86 33 Use the above datato compute the Values mthe Veenumbex summary a M1n1mum 0 lower quaml 7 5gtmed1an 34 upper quamle 55gtmax1mum b M1n1mum 0 lower quamle 11gtmec1ur1 33gt upper quarule atgt max1mum e M1n1mum0gtlowerquaml 85gtmed1an 1 53gtmax1mum d M1mmum ogt lower quaml 55gtmed1an lmpperquaml sumaxrmum e M1mmum0gtlowerquamler 4gtmed1anr40gtupperquamle ax1mu ANS A REF Seetrerr34AP 15 summary belov M1n1mum 50 Lower Quamle 59 Medun 75 Upper uamle 32 Max1mum 39 Buxplut1 u anew seesaw anew 4amp7 a Buxp1ut5 E An SD 6 7n an an 111111111 12111311 b onplotz c onplotz d onplot4 e onplots ANs E REF Sectlonz4AF 15 n t u m A A clevratlon 15 200 gallons What 15 the approxrmate value of the 92th percenllle7 e L300 gallons ANS A REF SectlonzsAF 17 A l n messagessent ANS E REF SectlonzsAF SHORTANSW39ER 18 Answer each of the followlng questlons m a few sentences 3 Why was 2 xi 2 ratherthan 2 xi chosen to be used ln bulldlng39he formula for the vananoe7 b Why 15 s more commonly used than 3 as a more useful measure ofvanabllllw a X Li 1 chosen over when uslng f to estlrnate n27 2 a Why was m d What factor should be conslclerecl when chooslnghetween the rnecllan orrnean as a clescrlptlon ofthe center ofa clata setv 3 Because 2 x 3 will always be 0 b Because it is in the same units as the original observations c Because on average dividing by n l tends to give a value closer to 62 than dividing by n d If a distribution is symmetric then either the mean or median can be used as a measure of center However if the distribution is not symmetric then the median should be used since it is more resistant REF Section 33 AP 19 A common topic of study among biologists who study social insects is colony integration ie the ways members of a society interact with and in uence each other Previous research suggests that the queen of a wasp nest seems to encourage worker activity That research is anecdotal and quantitative information is lacking The following data were gathered from wasp nests in California and Iowa The nests were studied very early in their development so each wasp could be individually identified using standard marking procedures and their activity levels monitored reliably The table below contains the proportions of time spent on the nest for 12 randomly selected colonies in Iowa The colony numbers are for identification in the table only There is only one queen per nest so the proportion is for her only The workers proportion is the average proportion for all the worker bees in the nest Queens and Workers Proportion of Time Spent on Nest Colony Queen Workers Colony Queen Workers 0 88 081 7 094 0 63 2 0 90 058 8 0 78 0 68 3 0 99 054 9 0 95 0 66 4 0 64 079 10 0 97 0 56 5 l 00 057 11 0 98 0 59 6 072 052 12 089 055 a Construct a comparative back to back stem amp leaf plot of the proportions of time spent on the nest by Queens and by Workers for these colonies b V Using your plot in part a describe the differences and similarities in the distributions of the proportion of time spent on the nest by workers and queens 505 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part ANS a Queen Worker l 5 l 24 l 5 l 56789 4 l 6 l 3 l 6 l 68 2 l 7 l 8 l 7 l 9 l 8 l l 98 l 8 l 40 l 9 l 7 l 9 represents 079 9875 l 9 l 0 l 10 l b The shape of the Queen39s distribution is single peaked and negatively skewed while the Worker39s distribution is single peaked and positively skewed The center for the Queen39s distribution is much higher than the Workers median 92 vs 585 Finally the spread for the Queen39s distribution is a little larger than the Worker39s range 36 vs 29 lQR 145 vs 115 REF Section 33 AP Exhibit 32 In 1990 the New York Times reported the average number of square feet per standing passenger in 1987 and 1988 for 19 subway stops Although the sampling method was not reported we will presume that these data represent a random sample of days during the morning and evening rush hours The NYC Transit Authority managers attempted to improve the space problem on subway cars more space is better trust us by adding cars to trains during the rush hours They gathered the 1988 data to check on their efforts after one year The data are in the table below Packed in at Rush Hour Sq Ft per standing passenger 506 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 22 19 36 32 24 21 38 27 18 22 37 43 20 Refer to Exhibit 3 2 a V Construct a comparative stem amp leaf plot of the space per standing passenger for the morning rushes of 1987 vs the morning rushes of 1988 b Using your plot in part a describe the differences and similarities in the distributions of the morning standing room for the two years ANS a 1987 1988 98 1 5899 444322 2 011122 955 2 89 421 3 3 7 3 99 0 4 14 8 4 5 5 5 l l 8 represents 18 sq ft per standing passenger 6 99 6 7 7 8 6 b The shape of both distributions is single peaked and positively skewed The center in 1987 is slightly higher 1987 median 25 and 1988 median 22 The variability is also similar however 1988 has a larger range because of an unusually high value 86 and it also has a higher lQR 1987 14 and 1988 19 REF Section 33 AP 21 Refer to Exhibit 3 2 The MTA guidelines in 1987 specified a minimum of 3 square feet per standing passenger The engineers would like to report standardized measures z scores of this target value That is for each year and time of day they will report how far away the target value of 3 feet is relative to the different distributions a Consider the original passenger space data for the morning rush in 1987 used in Exhibit 3 2 What are the mean and standard deviation for the sample HI 0 b How many standard deviations abovebelow the mean is the target value of 3 feet for the distribution in part a 507 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part a f 324 sq ft per standing passenger s 150 sq ft per standing passenger b 2 716 thus the target value of 3 is 16 standard deviations below the mean REF Section 35 AP 22 The data in the table below are the changes in the amount of space available to standing passengers at the 19 stops between 1987 and 1988 Changes in the space Per standing passenger Partial summary of change data In the table below summary information is presented for these data Quartiles Lower Upper Time Quartile Median Quartile AM 70 9 70 3 04 PM 71 2 70 2 06 508 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part Mulls and Standard dwia mls far dung data c DAV r0121 1 766 1089 4784 Dom forget to check for oulllers successful Remembergt more space 15 better Thelr ehglheers had suggested that lhe speclflc aspecls othe plot lh pan a suppon your ahswerv dlrrerehces lh success between lhe mommg rush and lhe a emoon rush ANS a Senumbersummary AM ezro 9701mm 5oulllers 4er 4 5 Senumbersummary PM e5 lgtel zfo 2gt o a 15 9 anthers e5 L5 zgt 2 lgt 15 9 b ade a m PM lhe AM would show a blgger rhcrease lh avallable space lhah lhe PM decreased overall Thls 15 lndlcated by lhe hegauve medlahs AM e0 z and PM e0 2 for both dlstnbullons There were some Stations where lhe avallable space moreased a for AM and 2 for PMgt but overall lhere seems to be less space durlngbo39h ume perlods REF Secuoh z 4 AP 23 Astronomers are interested in the recessional velocity of galaxies that is the speed at which they are mov1ng away from the Milky Way The accompanying table contains the recessional velocities for a sample of galaxies measured in kmsec Negative velocity indicates the galaxy is moving towards us Recessional velocities km sec 170 150 290 500 7130 920 770 500 7220 960 200 500 290 850 200 800 300 1090 650 A in V Calculate these numerical summaries The mean The standard deviation The median The interquartile range b Construct a skeletal box plot for these data c Judging from the data and your responses in parts a and b would you say this distribution is skewed or approximately symmetric Justify your response using appropriate statistical terminology ANS a mean 41842 standard deviation 38184 median 300 lQR 800 7170 630 b 5 number summary 7220 170 300 800 1090 510 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part EEI 1 1 1 1 1 1 1 250 0 250 500 750 10001250 dmanoe fromthe medmn to me maxmum REF Semen 14 AP 24 m vo1urr1esgt1mrrfgt r r n1 dh h 1171171 are summary staumcs farthese am Acnm Statistics 13115110 V 1ue 2 ean o edmn 2 1 Dev 5 1mmum z 105 51 Quamle 1 rd Quamle 4 z a whether euurers are present 1n are data b ANS 3 Usmg your procedure from panagtdelerm1ne rrmere are anthers 1n mese data anypans um are more than 1 5 mterquamle ranges above me Lh1rd quamle b oull1ersltll154 e 27 oull1ersgt4 z15lt4 ze1 1 91 There are no euurers omhe low end smoe mere are no values less than 4 7 Howevergt mere wlofffor anthers 9 1 REF Semen z 4 AP 25 The data in the table below are from observations taken on Roman coins dating from the first three centuries AD Historians believe that different mints might reveal themselves in different trace element pro les in the coins these coins are known to have been minted in Rome The technique of Atomic Absorption Spectrometry was used to estimate the by weight of various elements in these coins the by weight that is gold is presented here Roman Mint Gold Content bv quoteight 022 038 024 038 020 043 024 036 021 032 023 042 018 047 015 050 017 028 017 a Calculate these numerical summaries The mean The standard deviation The median The interquartile range b V Construct a skeletal box plot for these data c Judging from the data and your responses in parts a and b would you say this distribution is skewed or approximately symmetric Justify your response using appropriate statistical terminology ANS a mean 292 standard deviation 1 11 median lQR387 2 18 b 5 number summary 15 2 24 38 5 512 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part ddstanoe fromthe medmn to me max1mum REF Semen z 4 AP 25 ohm summary mums are gwen 1n the table below anmMint Lud Cnntmt quot1 weight Statistic V m 2 ea 0 1 ed1an o 2 1 Dev 0 5 1n1mum o 9 ammum 1 9 stQuamle o 1 rd Quamle o z a whether euurers are present 1n the data b Usmg your procedure from panagtdelerm1ne rrmere are euurers 1n these data ANS anypmn39s 11131 are more than 1 5 mterquamle ranges above the Lh1rd quamle oull1erslt 4171 5 727 41 oull1ersgt 7215lt7ze 41 b 21 There are no eudrers omhe low end smoe mere are no values less than 7 7 Howevergt mere wtofffor euurers 1 21 REF Semen z 4 AP 27 In order to attribute changes in nest activity to the active in uence of the queen 9 nests were randomly selected for experimental treatment The normal activity of the nests were measured and treatments were administered as described below Queens and Workers Experimental Treatments Normal treatment The observations were made of the undisturbed state of the nest as originally located Queen removed The queen was removed from the nest for about an hour Queen cooledinactive The queen was removed to a cool environment making her inactive and returned to the nest thus she is present in the nest but not able to interact with the worker wasps The data for the control treatment and each of the experimental treatments is given in the table below The Activity Levels are the average proportion of active nest time for workers who were present in the normal and two experimental treatment periods For example 050 would mean for that nest the average amount of time the workers were actively working was 050 of the available time during that treatment The colony numbers are for identi cation in the table only Workers Activity Levels Normal Queen Cooled Partial summary of data Treatment Lower Quartile Median Upper Quartile Normal 0135 032 Q Removed 017 023 032 Q CooledInactive 0055 014 0265 a Construct comparative box plots of the active nest times for a normal b Queen removed and c Queen CooledInactive Note since the data are proportions there are no actual units for the data b Two current theories about the queen s interaction with workers are that A the queen increases worker activity by her mere presence or B she increases worker activity by 514 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part c What are the mean and standard devratron of the proportron ofworker amvrty for undrsturhed wasp nests d One of the nests Colony 4 has a proportron ofworker amvrty of o 45 How many standard devratrons abovebelow the mean rs the worker attmty level m thrs nestv ANS 3 use E me P g me i i n27 lt mi N Go OR Tteatmem Srnumbersummanas N 05gt 125gt 22gt 445gt 59 QC ozgt 055gt 14gt 155gt 27 QR 05gt 11233140 and QR The data do not support theory A smoe the treatment wrth the smallest rnedran 15 when the Queen was rnattrve but stru present QC d z o 9gt thus the observatron om 45 rs o 9 standard devratrons above the mean REF Sectron z 4 AP 28 Consider a study in which the heights ofa sample of 1000 high school seniors were recorded The mean height is 70 and the standard deviation of the heights is 3 It is observed that the height distribution is approximately normal a Approximately what percent ofheights in this sample would exceed 79 b What is the approximate percentile ofa senior who is 73 tall c When the data were summarized the value of the first quartile was written down but then smudged There is general agreement that the writer meant to indicate either 66 or 68 Which of these values is most likely the correct one Justify your answer with appropriate statistical reasoning ANS a 15or0015 b 97mpercentile c Since a height of 67 is one standard deviation below the mean we would expect only 16 of observations to be below 67 Since 25 of the observations should be less than the first quartile the rst quartile must be 68 REF Section 35 AP Exhibit 31 In recent years there has been considerable discussion about the appropriateness of the body shapes and proportions of Ken and Barbie dolls These dolls are very popular and there is some concern that the dolls may be viewed as having the Hideal body shape potentially leading young children to risk anorexia in pursuit of that ideal Researchers investigating the dolls39 body shapes scaled Ken and Barbie up to a common height of 17018 cm 539 7 and compared them to body measurements of active adults Common measures of body shape are the chest bust waist and hip circumferences These measurements for Ken and Barbie and their reference groups are presented in the table below Doll and Human Reference Group Measurements cm Ken Barbie Chest Waist Hips Chest Waist Hips Doll 750 565 720 823 407 727 Human E 912 809 937 903 698 979 Humans 48 98 68 55 47 54 For the following questions suppose that the researchers39 scaled up dolls suddenly found themselves in the human world of actual men and women 516 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 29 Refer to Exhibit 3 1 a Convert Ken39s chest waist and hips measurements to z scores Which of those measures appears to be the most different from Ken39s reference group Justify your response with an appropriate statistical argument b The z scores for Barbie39s Chest Waist and Hips when compared to active female adults are approximately 714 762 and 747 respectively Do these z scores provide evidence to justify the claim that the Barbie doll is a thin representation of adult women Justify your response with an appropriate statistical argument c If men39s waist measurements are approximately normally distributed based on the sample above what is the approximate percentile of a 100 cm waist a chest 2 73375 waist z 7249 hips z 73l9 Thus it appears that Ken39s chest measurement is the most different since it is farthest from the mean human measurement in terms of standard deviations b Yes since all of the z scores are negative Barbie39s measurements tend to be below average ie skinnier This is especially true of her waist which is 62 standard deviations below the mean c A waist of 100 cm is almost 2 standard deviations above the mean 2 195 so it would be approximately the 973911 percentile REF Section 35 AP 30 Refer to Exhibit 3 1 a Convert Barbie39s chest waist and hips measurements to z scores Which of those measures appears to be the most different from Barbie39s reference group Justify your response with an appropriate statistical argument b The z scores for Ken39s Chest Waist and Hips when compared to active male adults are approximately 734 725 and 732 respectively Do these z scores provide evidence to justify the claim that the Ken doll is a thin representation of adult men Justify your response c If women39s waist measurements are approximately normally distributed based on the sample above what is the approximate percentile of an 80 cm waist ANS 3 chest 2 7l45 waist z 7619 hips 2 7467 517 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part Thus it appears that Barbie39s waist measurement is the most different since it is farthest from the mean human measurement in terms of standard deviations b Yes since all of the z scores are negative Ken39s measurements tend to be below average ie skinnier c A waist of 80 cm is slightly more than 2 standard deviations above the mean 2 217 so it would be approximately the 98th percentile REF Section 35 AP 3 1 Grey Kangaroos are large social marsupials indigenous to Australia As part of a study of the development of these creatures biologists have measured various aspects of their skeletal structure A sample of 148 palate widths was taken from skeletal remains and the data is presented in the stem and leaf plot below The distributions of skeletal measures are generally thought to be approximately normal which is consistent with the stem and leaf plot for this sample The display uses five lines for each stem Thus H2tlH is the stem for palate widths of 22 and 23 quot2 quot for 24 and 25 H2slH for 26 and 27 and so on The t then stands for leaves that are twos and threes the f39 for leaves offours and fives etc The mean palate width of this sample is 26 cm and the standard deviation is 03 cm Palate Width Grey Kangaroos ll0lcm Nl24 ls 77 1 89 2 01111111111 2t 222222222223333333333333 2f 444444444444444455555555555555 2s 6666666666667777777 2 88888888888889999999999999 3 0000011 3t 223 A in V If this sample is a good representation of the population of Grey Kangaroos approximately what percent of palate widths in this sample would exceed 29 cm b V What is the approximate percentile of a palate width that is 20 cm c One measure of variability is the length of an interval that contains the middle 90 of the values of a distribution For these data how long is that interval 518 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part ANS a 101240806 or 8 b 5124 0403 thus a width of 20 cm is approximately the 4th percentile c 29 21 an interval of length 8 REF Section 35 AP 32 The Territory of Iowa was initially surveyed in the 183039s The surveyors were very careful to note the trees and vegetation it was believed at that time that the richness of the soil could be measured by the density of trees encountered The sample of Ash tree diameters from the original survey of what is now Linn County Iowa is presented in the stem and leafplot below The display uses ve lines for each stem Thus ltl is the stem for diameters of 12 and 13 quot111 for 14 and 15 lsl for 16 and 17 and so on The t then stands for leaves that are twos and threes the 1quot for leaves offours and fives etc The mean diameter of ash trees in this sample is 11500 inches and the standard deviation is 3842 inches Linn County Trees in 1830 Ash Diameters 110 10 inches N 102 0 0t 2 0f 44 0s 666777 0 8888888888888888888999 l 000000000000000000 1t 22222222222222222222222 1f 444444444445 1s 666666 1 8888888888 0 a What is the approximate diameter of an ash tree at the 20th percentile in this distribution b The Empirical Rule would suggest that 68 of ash tree diameters are between what two values ANS a 20 ofn 102 is 204 so we are looking for the 203911 value in the ordered list which is 8 b 7658 and 15342 REF Section 35 AP 519 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 33 The Territory of Iowa was initially surveyed in the 183039s The surveyors were very careful to note the trees and vegetation it was believed at that time that the richness of the soil could be measured by the density of trees encountered The sample of hickory tree diameters from the original survey of what is now Linn County Iowa is presented in the stem and leafplot below The display uses ve lines for each stem Thus H1tlH is the stem for diameters of 12 and 13 quot111 for 14 and 15 lsl for 16 and 17 and so on The t then stands for leaves that are twos and threes the 1quot for leaves offours and fives etc The mean diameter of hickory trees in this sample is 11849 inches and the standard deviation is 3995 inches Linn County Trees in 1830 Hickory Diameters 11010inches N73 0t 45 666666677 0 88888888999 00000000 222222222222222 4444444444445 1s 666 1 88888888888 2 0 2t 2f 2s 2 O we b b A b 39gti gt What is the approximate diameter of a hickory tree at the 20th percentile in this distribution a V b The Empirical Rule would suggest that 68 of hickory tree diameters are between what two values ANS a 20 ofn 73 is 146 so we are looking for the 153911 value in the ordered list which is 8 b 7854 and 15844 REF Section 35 AP 520 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part Chapter M Data TRUEFALSE 1ten average 1 mmeases as x moreases the correlauon coef mem 15 posmve ANS T REE Settren 4 1 AP Pearson s correlauon noemtrentgt y does not depend on the unrts of measurement of the two vanab1es ANS T REE Sectmn4 1 AP The va1ue of Pearson s y 15 a1ways between 0 and 1 ANS F REE Settren4 1 AP 1h 15 t1ese to 1gt then the pews he t1ese to a strargnt lme w1Lh a posmve s1epe ANS T REE Sectmn4 1 AP The s1epe othe 1east squares lme 15 the average arneuntby whmhy moreases 25x mmeases by one unrt ANS T REE Sectmn 4 2 AP The 1east squares lme passes througq the pmm ANS T REE Settren 4 2 AP The slopes of the 1east squares hues for predmmg y mm x and the 1east squares lme for predmmg x from ygt are equa1 ANS E REE Sectmn 4 2 AP 1t 14 1 the standard devratmn ofy 15 equa1to the standard devratmn of the resrdua1s ANS E REE Settren4 24 2 AP The hrgner the va1ue of the teemtrent etdeterrnrnatrengt the geater the ewdmoe for a tausa1re1at1edsh1p betweenx and y ANS E REE Settren4 2 AP The standard devratren aboutthe1eastsquares11ne 15 reuguy the lypwal arneunt by whmh an observauon devrates from the 1east squares lme ANS T REE Sectmn4 2 AP 521 11 The value of the residual plus 339 is equal to y ANS T REF Section 43 AP 12 The coefficient of determination is equal to the positive square root of Pearson39s r ANS F REF Section 43 AP 13 A transformation or reexpression of avariable is accomplished by substituting a function of the variable in place of the variable for further analysis ANS T REF Section 45 AP MULTIPLE CHOICE 14 Which of the following indicates the range of possible values for Pearson s correlation coef cient r a D lt r lt 1 b 1 lt r lt 1 C 1 5 r S 1 d 1 539 r lt 1 G 1 lt r S 1 ANS C REF Section 41 AP 15 Of the following which is true ofPearson s correlation coefficient r a The value of r does not depend on the units of y and x b r 0 indicates a perfect correlation between x andy c r cannot be less than 0 or greater than 1 d The value of r depends on which of two variables is labeled x e r is greater than 10 unless the points on a scatterplot line up exactly ANS A REF Section 41 AP 16 Which ofthe following indicates the range ofpossible values of the coefficient of determination r 7 21 051931 b DU 6 49351 d 1ltr2lt1 6 1ltr2lt ANS A REF Section 43 AP 522 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part l7 tt ml t h a an r Thex values were transformed uslng a squareemot transrolrnatlongt and a scatterplot of 1 versus x x betweeny andx was y e 24 e 3x What 15 the preclntecl value ofywhen x 16 7 a e24 b 15 0 l2 d lz ANS c REF Sectlon 4 5 AP 12 between experlence and the amount ortlme requlred to complete an assembly task Assembly tlme measured for each worker The resultlng clata on y tlme to complete assembly and x number an an 70 to so an an no so 75 mo 25 no US Predlctor Coef SECoef T P Constant 24 522 5 an 15 l2 o 000 x en zntll 004952 ea 13 o 000 5979097 Fawns ReSqadJ504 o a 81 am b 90 5 mm 1104 d 120 7 mm 150 2 Am A REF Sectlon4 2 AP n x e the weight of a pickup truck pounds and y distance in feet required for a tmck traveling 40 miles per hour to come to a complete stop for 30 trucks was used to fit the least squares regression line 7 e 26 a 05x Which of the following statements is a correct interpretation of the value 005 in the equation of the regression line nnaverae p quot 39 M the truck b nnavera e m t r l c The correlation coefficient for this data set is 005 d nnamraem o 439 in 439 39 weight e p 39 39 39 39 39 39 p39 439 quot 139 drelinear relationship between stopping distance and truck weight ANS D REF Section 43 AP 20 Data were collected on y price ofcar in dollars and r e age of car in years for each car in a sample of 60 used Toyota Camrys A scatterplot showed a negative linear relationship between r and y The least squares regression line was fit and the r value was computed If r2 u 55 which of the following is a correct statement a The correlation coefficient is positive 7 055 Lfthe leastsquar s he is used to predict car price based on number ofmiles driven predictions should be within 055 of the true price 0 There a cl d r u ax quot L ofmilesdxiven I 39I Aquot D a 931 r I I FF e p 39 39 39 39 quot 139 drelinear a L a ANS E REF Section 43 AP 21 mi Rum L quot y axes For which scatterplot is the relationship negative a d stamina swamp 524 in m A m Scarrarpluila 5crttcrplan c Scurarplor c ANS A REF Section 43 AP Data on x x the weight of a pickup truck pounds and y distance in feet required for a tmck traveling 40 miles per hour to come to a complete stop for 30 trucks was used to fit the least s uares regression line 26 a 05x w 39ch of the following statements is a correct interpretation of the value 26 in the equation of the regression line nnamraem o r 39 ealil 439 3939 6 o z a i a 1 c d ilh linear relationship between stopping distance and tmck weight u o a the range of the data used to fit the regression line ANS E REF Section 42AP 23 Twentyfive assemblyline workers participated in a study to investigate the relationship 39 39 A L 39 1 39 l 39 39 task sembly time in minutes and number of months the worker had been employed on the assembly line were measured for each worker The resulting data on y time to complete assembly and x number 4 u u i m i r i uulyul new 525 uw m A m 10 Predmor Coef s E Coef T P Constant 24 523 5 an 15 12 o 000 x in mm 004952 3 o 000 504 s 9 79097 Rqu 52 0 RquadJ ANS E REE Secuon4 2 AP SHORT ANSWER 24 What 15 n mauhe Pearson correlauon coemmem quanunesv ANS between two vambles REF Sectxm41AP 15 me quantity 2 szy 7 ANS The sum 15 negame REF Sectxm41AP 25 the duahtltygt 2 szy 7 s The sum 15 pesltlve REF Sectleh 41A othe prepertles of Pearson s y 15 The value on does not depend on the umt of 27 One measurement for ether vanable H lh your own wordsgt what does th5 meahv ANS t t p t exactly the same lthey are measured m cenllmelers ahd kllograms REF Sectleh 41A 120 vanables 15 labeled as x lh your own words what does ths meahv ANS h h h p l REF Sectoh4 1 AP 29 The breedlngsuocess ofblrds that heat on the gound can be affected by the depth of quotnNeslSucctss Vs SnnwDepMcm amle 8 we 00 snawpamw llhe uslhg the axes above Show any calculatlohs h the space below b gaph above plok 2 polhts and slretch the reslcluals assoclatecl wth those polhts ANS a sketched llhe should lhtersect Lhayaxls 3155gtandthellney10 at about 491 t least squares llhe REF Sectloh42AP MSC Sectlohu 20 1 u Central Flohclagt uslng blrd decoys to test the rellablllty of the process on cullm Actual counlvs AM Mail cm 5 m 5 a 25 1 helmquot cm a A U9241 A vltm l m gaph above Show any calculatlohs h the space below b gaph above plok 2 polhts and slretch the reslcluals assoclatecl wth those polhts ANS 3 Sketched line should intersect the y axis at about 71 and the liney 25 at about 26 b Sketch should show two vertical segments each extending from a point to the sketched least squares line REF Section 42 AP 31 The data below were gathered on a random sample of 5 basking sharks swimming through the water and lter feeding ie passively letting the water bring food into their mouths Mean speeds for basking sharks Body Length Mean speed meters 40 089 45 083 40 076 65 094 55 094 a What is the value of the correlation coef cient for these data b What is the equation of the least squares line describing the relationship between x body length andy mean speed c Lfthese sharks are representative of the population of basking sharks what would you predict is the mean speed for a lter feeding basking shark that is 50 meters in length Show any calculations below d The largest basking shark in the sample is measured as 65 meters long Theory predicts a maximum length of about 1226 meters Would it be reasonable to use the equation from part b above to predict the mean lter feeding speed for a 12 meter long basking shark Why or why not S a r 07492 b 3 061 00534x c 061 0053450 88 msec d No it would not be appropriate to use this equation to predict the mean speed of a shark that is 1226 meters long This would be an extreme extrapolation from the data that has been provided and is an unreliable procedure REF Section 42 AP 529 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 32 The data below were gathered on a random sample of 7 male black footed albatrosses of known age In an effort to monitor diseases of these animals biologists would like to be able to estimate the age of animals that have died by attening their gonads and measuring the resulting area Gonad size vs Age in Blackfooted albatrosses Gonad Size Age sq mm Years 42 142 60 475 20 067 96 23 64 24 052 27 2 35 27 14 a What is the value of the correlation coefficient for these data b What is the equation of the least squares line describing the relationship between x Gonad Size andy Age c If these are l 39 o the r r what would you predict to be the age of a male albatross with a gonad size of 50 sq mm397 Show any calculations below d The largest albatross gonad size in the sample was 96 sq mm with an age of 2364 years These animals are thought to live for up to 40 years Would it be reasonable to use the equation from part b above to predict the age for a gonad size of 150 sq m Why or why not a r 0926 b j 7699 0283x C 7699 028350 715 years d No it would not be appropriate to use this equation to predict the age of this albatross This would be an extreme extrapolation from the data that has been provided which is an unreliable procedure REF Section 42 AP 530 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part Exhibit 43 Paleontology the study of forms of prehistoric life can sometimes be aided by modern biology The study of prehistoric birds depends on fossil information which typically consists of imprints in stone of aprehistoric creature39s remains To study the productivity of an ancient ecosystem it would be useful know the actual mass of the individual birds but this information is not preserved in the fossil record It seems reasonable that the biomechanics of birds operates much the same today as in the past For example relationship between the wing length and total weight ofa bird should be very similar today to the relationship in the distant past The wing lengths of ancient birds are readily obtainable from the fossil record but the weight is not Assuming similar biomechanical development for ancient birds and modern birds a regression model expressing the relationship between wing length and total weight of a modern bird could be used to estimate the mass of similar prehistoric birds and thus gauge some aspects of the ancient ecosystem Data is available for some modern birds ofprey Speci cally data on the mean wing length and mean total weight of species ofhawk like birds ofprey is given below Wing length and total weight of modern species of birds of prey Wing length Total weight Bird species cm kilograms Gypsfulvus 698 727 Gypaet us barbat us grandis 7 l 7 539 Catharist a atrat a 5 02 170 Aguila chrjysat us 682 371 Hieraeus fasciat us 5 6 0 206 Helot arsus ecaudat us 512 210 Geranoat us melanoleucus 5 l 5 212 Circat us gallicus 5 3 3 166 Buteo buet o 404 103 Pernis apivorus 451 062 Pandion haliat us 496 11 l Circus aeruginosos 4 13 068 Circus cyaneus female 374 0472 Circus cyaneus male 339 0331 Circus pygargus 359 0237 Circus macrurus 357 0 38 6 Milvus milvus 507 0927 33 Refer to Exhibit 4 3 What is the equation ofthe least squares line ANS W 535 01461 where Wis the wing weight andL is the wing length REF Section 42 AP 531 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 4 Refer to 5x11131144 Approxmalely what propomon othe vanab1l1ty 1n we1ghl1s explamed by me wmg 1mm ANS 1 205 REF Sect1on4ZAP 1214111711471 11 about d15play1ng 11 One pessrbrmy 15 chamcal analys1sgtwh1chm1gqlg1ve some evrdeme about rewrded lemony usmg ammo 201d ram as a predmor mum ma ra n and Amm 201d 2 Ten 1 1 1 11 1 o 1 1 1 2 z 1 2 1 41 1 z 2 z 15 1 1o 1 35 Refeno Exh1b1t4el What 15 me equauon othe leaslrsquaras lme7 ANS i 5 55 e 1 thgt where T15 me lmacny and R 15 me ammo 201d ram REF1 Semen 4 2 AP 36 Refer to Exhibit 4 1 Approximately what proportion of the variability in tenacity is explained by the amino acid ratio ANS r2 636 REF Section 43 AP 37 In the 19th Century venereal diseases were the major preventable diseases striking soldiers far from home During the American Civil War the United States Army kept records on soldiers diagnosed with syphilis and gonorrhea An analysis of the incidence of these diseases is presented below lncidence is the rate of increase in the number of cases for these data the incidence is number of soldiers per 100000 per month Summary statistics from Regression Analysis Incidence of syphilis and gonorrhea for the years 1861 1865 I I Syphilis I Gonorrhea E 2697 3653 s 0980 1206 r0914 EI6211124S a If at a particular point in time the incidence rate for Syphilis is one standard deviation above the mean what would be the predicted incidence rate for gonorrhea ANS a quot3 U 211124269 1980 4715 or if a point is 1 standard deviation above the mean for Gonorrhea it should be 0914 standard deviations above the mean for syphilis G 3653 19141206 476 REF Section 42 AP 38 The Des Moines Register recently reported the ratings of high school sportsmanship as compiled by the Iowa High School Athletic Association For each school the participants and coaches were rated by referees where 1 superior and 5 unsatisfactory A regression analysis of the average scores given to football players and coaches is shown below 533 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part FBP nicipzmts Vs FBCnmlm myme 2 3 FBEaaches Linear m FBPanicipanm 0 902 0 568 FBCoaches Summary ol F it RSquare 0 452 RSquare Ad 0 450 s 0 355 Analysis orvmanee Source DF ss MS F Rauo Model 1 37 505 37 505 298 2723 EH01 362 45 518 0126 Prob gt F c Total 363 83 022 lt 0001 0 Interpret the Value erme coemcxem 0f detexmmauon c Interpret the Value erme standard devxauon about the least squares lme ANS 4 Conelatmn ls 452 672 ms mchcates a moderately suong lmear relauonshxp between rated spoxmansmp for pamclpanw and coaches 2 Z panmpants can be explamed by chffexences m coaches spoxmnanshxp S lme REF Secuon 4 3 AF 39 Hrgn Sch I m t t orea partrcrpants were rated by referees where uperror and 5 unsatrsfactory A regessmn V mu39 as a 757 1 4 5 2 2 5 5 s Linear Fit WrestSpectators 0 667 0 701 Wrestlers Summary anit RSquare 0 467 RSquareAd 0 465 s 0322 Analysis oI Variance Source DF 53 MS F Ratro ModeI I 26 437 26 437 254 2274 Error 290 30157 0104 Probgt F c TotaI 291 56 594 lt 0001 a Interpret the correIatron between the mung of spectators and wrestlers b Interpret the coeffment of deternunatron c Interpret the value othe standard devxatmn about the Ieast squares hne CorreIatron Is a 457 e 633 Thhs rndrcates a rnoderaterstrong hnearreIatronshrp between ratedsportsnranshrp for spectators and particxpanns b 2 67 means that about 47 ofthe observed dIffermces In sportsnranshrp among spectators can be explade by drfferences In panIpraan sportsmanshrp c s hne REF Seaman 43 AP 40 When children and adolescents are discharged from the hospital the parents may still provide substantial care such as the insertion of a feeding tube through the nose and down the esophagus into the stomach It is dif cult for parents to know how far to insert the tube especially with rapidly growing infants It may be possible for parents to measure their child39s height and from that calculate the appropriate insertion length using a regression equation At a major children39s hospital children and adolescents39 heights and esophageal lengths were measured and a regression analysis performed The data from this analysis is summarized below Summary statistics from Regression Analysis Height cm and Esophageal Length cm Esophagus Height Length E 3 34cm 1245cm s 35cm 19cm r 0995 E 11476 0181H a For a child with a height one standard deviation above the mean what would be the predicted esophageal length b What proportion of the variability in esophageal length is accounted for by the height of the children and adolescents c From the information presented above does it appear that the esophagus length can be accurately predicted from the height of young patients Provide statistical evidence for your response ANS 3 E 11476 01811245 19 3740 or if a point is 1 standard deviation above the mean height it should be 0995 standard deviations above the mean esophagus length E 34 099535 3750 b r2 09952 09900 About 99 of the variance is accounted for by the height ofthe children and adolescents c Since 99 ofthe variance is accounted for by the height in the prediction the predictions should be very accurate compared to the variability of the esophageal length To assess the prediction in any absolute sense we would need to know the value of SE REF Section 43 AP 536 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part Exhibit 475 l m h a lnvestrgators studled ll oolns known to have been produced by localmln39as ln an attempt to m t m presented below quotoLead v5 quotuGVDIlI bane E u 25 e 2Equot 25m 3m 35m eon 18 Refer to Exlubltates a What 15 the equatlon of39he least squares best at llne7 b sketch the best t llne on the statterplot c What 15 the value othe torrelatlon toemtlentv Interpret ths value d ANS 3 el 84 l 346 where L 15 the lead content and G 15 the gold content u gaph wlthregessron llne c y o 592 Thls lndlcates a moderately strong llnear relatlonshlp between Lead and ld d 2 n a the gold content REF Sectlon4 2 AP 41 years AD calwlate the predlcted lead content Be sure to use correct notatlon and unlts u Calculate the resldual fothls coln Be sure to use correct notatlon and unlts 0 l t t would colns mlnted in Rome have to dlrter from locally mlnted wm57 ANS 3 en184l34n3nnzl9lead b resldual Xi H l7e n zlszeu MEDn 0 related Ifa com ofunlcnown ongm 15 added to me saauapm and fell on or near me V R q m Lhelocalmmt REF Sectxon4ZAP Exhibims A nh mu V m pessdale factors m xdmufymg other cams as havmgbeen mmced m Rome The gold and lead q y m y N data 15 presented below Gala and Lud Cement quoteLeml vs quotMom Dar I I su an an 42 Refer to ExhlblMe a What 15 the equatlon othe least squares best t llne7 b slretch the best t llne on the scatterplot c What 15 the value othe correlatlon coemclentv lntelpretthls value l and e 3 5356gt where L 15 the lead content and G 15 the gold content b rraph wrthregessron llne 150 zuu 250 6M6 re 0 549 Thls lndlcates a moderately negatlye llnear relatlonshlp between Lead and oGold d t n m Lhegold content REF Sectlon4 2 AP 42 Suppose that the colns analyzed ln Exhlblt 4 are representatrye of the metallurglcal content of colns mlnted In Rome dunng the rst 200 years An a If a Roman com 15 selected at raddorngt and lts gold content 15 o 10 by werghtgt calculate the predlcted lead content Be sure to use correct notatlon and unlts Calculate the resldual fothls com Be sure to use correct notatlon and unlts 0 wln57 ANS 3 Lquot l we 3 dzs 2n n 579lead 89U579U311 were far from the lrnegt it would suggest that it was not produced or Rome REF Sectlon4 2 AP onrd and m l q a 4th gaders vlews on 42 personaluy lrallsgt chlldxen were asked to rate on a sporan scale eorre possessrng that Lrall is probably a boy someone possessrng that Lrallmlght be a boy 0 tell l someone possessrng that Lrallmlghl be aglrl 2 someone possessrng that Lrall is probably a glrl E boys raung for a glven lrau Male Ruling V5 Female Rnrmg P Male mm u P Female Rube Linur m MRatlng o 755 0 714 FRallng Summary of Fit RSquare 0 552 RSquare Ad 0 529 s 0 490 Analysis ol Variance Source DF SS MS F Ratio Model 1 5 6 5 63 23 45 Error 19 4 56 0 24 Prob gt F c Total 20 10 20 0 0001 a Circle the single point which representsthe most in uential observation What aspect of thispoint makes it the most ln uentlal b an tell by the girls The pledlctedboys average rating would be closest to which 0fthe 5 categories described above7 0 The traitsplotted above are those the researchers believe are posltlve halts such as mam ii ii aiiu p i andor regession analysis presented above are consistent with this thinkingv ANS 2 line would produce a large change in itsresidual To minimize the sum ofthe squares ofthe 7 m l b l l b l slope 0fthe line to increase significantly l E g 4 a s g l J n i Flfnmlln siting b Mlatlng7 765 71407 765 This is closestto the category mlghtbe a glll c Wm l i tm female numbers These would be belowthe graph 0fyx Shown on the gaph above All but one ortwo 0fthe points are consistent with thisthinlnng REF Section 4 3 AF 45 Assessing the goodness of fit ofa regression line involves considering different information and no single characteristic of data is suf cient for a good assessment Consider the characteristics below How does each contribute to an assessment offit That is for each piece of information what about it would indicate a good best fit line a The shape of the scatter plot b The correlation coefficient c The standard deviation of the residuals d The coefficient of determination a Points on the graph lined up in a pattern that is consistently increasing or decreasing rather than curved b Values ofr that are close to fl or 1 c Small value of the standard deviation of the residuals close to zero d Value ofr2 close to l REF Section 43 AP 46 Assessing the goodness of fit ofa regression line involves considering several things and no single characteristic of data is suf cient for a good assessment Consider the characteristics below How does each contribute to an assessment of t That is for each piece ofinformation what about it would indicate a good best fit line a The shape of the residual plot b The correlation coefficient c The demonstration of seriously in uential points d The coefficient of determination a A uniform cloud of points with no apparent pattern b Values ofr that are close to fl or 1 c Points that are potentially in uential extreme x values would lie close to the line calculated with these points omitted d Value ofr2 close to l REF Section 43 AP 543 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 47 n t l reoml spnhg 251 adult females Wth 492 wbs were captured as they le Lhelr da15gtand the kllogams to age or years resulted h the regressloh analysls below VeigJ r lkgt V Age yrs WzlthkV 5 1D 15 Ave vs Pnlynnmial Fit mgrst Weight 22 920 12134 Age 7 o 350Age Az Summary of Fit RSquare o 742 RSquareAdJ o 722 9 144 Analysis anarianu Source DF 55 Ms F Ratlo Model 2 4975 59 2427 25 19 7552 Error 10 157212 22 51 Prob gt F at Total 12 5M7 21 lt 0001 a 0n averagegt abouthow far off are the welgth othe matemal bears 7 That lsgt what 15 a modem by appealhg to the hrolmatloh pmvlded above ANS a s 914kg b The maxlmum value of the quadratlcmodel 15 around l5 or 17 years l5 25 REF Secllon4 5 AP 42 populatlohs myestrgatorsrepeatedlysampledsemohs ornyers m Ausu alla medlle lengvhs were measured m srze classes Crocs o o e o 2 meters m lengvh are m srze class lgt o z e o 5 meters 10 The captured crowdlles The output from thelr ahalysls 15 shown below Prol tcmtlme va ze Class a 6 o a m are class Pnlynnmial Fit DAgnFZ PrCap o 55 o 77class e o 01ClassAZ Smumary of Fit RSquare o m RSquare Adj 0 902 s o 052 Analysis of Variant Source DF 55 Ms F Ratlo Model 2 0249 0174 45 4295 Error 7 o 027 o 004 Prob gt F c Total 9 o 275 lt 0001 a slze cla557 b gt and ahalysls above ANS a l 922 b ms bellefappeal s to be tmegt slnoe the largest rowdlles appear to have the smallest REF Sectlon 4 5 AF Exhibit 472 AmrmAEldRmm 49 Refer to Exhlblt 472 What ls the lesultlng best t llne uslng thls model7 ANs 1397e7sllugmae REF Secllon45AP 50 at t Hts 5gt ANs i397e7sllugnlsz s REF Sectlon 4 5 AF 51 Refer to Exhlblmrl Does ll appear LhatLhe transformed model l5 no lmpmvanent over the r A r r m Q appropnale statlstlcal argummh ANS uahsrolmecl model REF Secuoh 4 5 AP Exhibit 4 lenth ls expohehual le W may or W we where Wlslhewlng Welghl and LlsLherng leng39h IeF olW rlulkrlayw uLe xlllc Welggllxg 52 Refer to ExhllmM For a wlng lehglh onhe data palm where L 55 o Hlemeu mommy what 15 the preclmecl blrd welghm show your work below ANS base 10 1035 natural logs logmU V WW 15000239550 or 3580078055 o 301 592 W 0quot zookg W HMZZOOkg REF Secuoh 4 5 AP 5 Refer to Exhlbll44 What ls the resultlng best t llne uslng the transformed model7 ANS luanW l EI H mm or lnW 73 68 H mm REF Sectlon 4 5 AP 54 m At llnearmodelv ANS h l model resldual plot lndlaates LhatLhe exponmllal model ts the data better Llnear Model Exponentlal Model REF Sectlon 4 5 AP 55 F r l h a as a percent For examplegt there are 10 horses in a goupgt a person in the plane may lyplcally l to a 9 up weregsthered u Undueaunt vs Group Siz far Harm and Dnnkzy Pa l t models The computer output rorthese models 15 glven belowgt and the reslduslplots follow 548 lugPabG lugPablugG Exponmual P ower Linur m Linur m LogU05850031Cvmuprze LogU04750440LogGS Resmua Exp Mnde lugPablugG Resldua power Mme 1 5n 2 an LagSlze b Use your calwlatlons frompan a to predlcnhe quotounderwunl for a goup srze 10 0 Generally speaklng whloh of the two moclelagt power or exporrehtralgt 15 better at predlmng the log Perch Underwum Provlde slallstlcal Justification for your home ANS a logrnO 05850031605850031100895 b Jule y 427 samerrnot perfectgt but acceptable The 2 value for the Exponmual 15 bettergt howevergt o 499 vs 0 227 for the powermodel The preclmecl values for the logqaemenl undercoum are clevratloh othe reslclualsgt o 155 vs 0 120 torthe powermoclel REF Sectloh 4 5 AP Exhibit 477 whlch they p l t turngt l t et A presented h the table below Bndy might vs Ham rang m npmmta u illszc v 39u Spldlx mus mammall H a w l Q models The computer output furthese transformed models and me residual plots follow Ruidnal Plat and Statis cal Analysis 7 zxpnnul al madll lugHabW Residual P101 3 2 E n E 72 n 25cm 5mm 75cm lunnn 125nm auuvwemma Lag Ham RangEVSW ight LogH ozsoo 0017221 W Summary 01 Fit RSquare o 229 RSquare Adj 0 202 o 940 Ruidnal Plat and Statis cal Analysis 7 Pawn mm lugHablqu Residual Flor 4 5 La EadWVelgM Lag Ham Rang vs Lag ngght Logai el 501 0 xgzLogm Summary of Fit RSquare 0591 RSquareAdJ 0574 s o 734 55 Refeno ExhlblMJ Forllre exponermlmoclel calwlatethepredlcted log Home Ragga for a Welghl of lOOOg ANS lugH REF Secuorl 4 5 AP 57 Refer to ExhlblMJ Gmerally spealurggt whlch onlre two models power or exponemlal ANS e one fothe exponmtlal moclelgt more or keeplng wth me ldeal The value for R 15 also much lllgrergt o 591 vs 0 229 for me exponmtlal moclelgt lndlcallng um me power model bener explalns me vanallon lnthe log values REF Secuon 4 5 AP 52 Refer lo ExhlblMJ These shrews lyplcally Wexgh 550g and lhelr home range 15 about 2 9 llamas explaln why or why not ANS Calculate the wordlnales othe pm on the power resldualplol lugH rmwtmzl DEE o 715010 89310g550 451 1 501 1447 0 334 plolpolnlal 2 74gt 70 224 Palm is plotted 21X on the resldualplol below a a a Logf adyiVnighl REF Semen 4 5 AP Chapter 05 Probab ity TRUEFALSE 1 A chance expenment 15 any actrvrty or srtuatron m whxch there 15 uncertamty oncemrng whmh ortwo or more possrble outcomes wru result ANS T REF Sectron 5 2 AP 2 Any couectron ofpossxble outcomes ofa chance expenment 15 called asample space ANS F REF Sectron 5 2 AP 2 An event consrstrng orexactly one outcome 15 called a srmple event ANS T REE Sectron 5 2 AP 4 The probabrhty of an event E can always be computed usrng the formulagt Pa 7 number ofouteomes favorable to E number ofouteomes rnthe sample space ANS F REF Sectron 5 2 AP 5 The c1assrca1 vrew ofpmbabxmy 15 based on the Law of Large Numbers ANS F REF Sectron 5 2 AP The event A or B mnst of an of the outcomes m both of the events ANS F REF SecuonS 2 AP 7 Two events are sard to be disjoint or mutuauy exclusrve when they have no outcomes m common ANS T REF SecuonS 2 AP 2 mwo events A and Egt are mutually evclusrvegt then PA and B PA ms ANS F REF SecuonS 2 AP 9 Two events are mdepmdent fohey cannot ocwrsxmullaneously ANS F REE SecuonS 2 AP 0 Two eventsgt E and Egt are mdepmdmt rt PE m e PUNE ANS F REF Sectron 5 4 AP ll The General Mulllpllcatlon Rule states that PEn D PE PU39U ANS T REF Secllon 5 5 AP 12 The General Addlllon Rule states that who e p5pnep5nm ANS T REF Secllon 5 5 AP MULTIPLE CHOICE lZ probablllty a l m l Atlanta wlll arnve on tlrne b ln the long mngt 25 othe tlrne ths pamwlar mgnt that the between Phomlx and Atlanta wlll arnve on tlrne 0 ln the l mngt 54 othe tlrne ths pamle mgnt that les between Phomlx and Atlanta wlll arnve on tlrne d ln the l run 54 othe tlrne ths pamwlar mgnt that les between Phomlx and Atlanta wlllnot arnve on time e ln the long mngt 54 othe tlrne ths pamwlar mm that the between Phomlx and Atlanta wlll arnve earllertnan expeaed ANS c REF Sectlons l AP l4 ths the 500 tlrnesgt now many nlnes do you expea to roll7 a about 57 ANS B REF Sectlons 1 AP develop an lnremonv l Ptne panent develops anlnfeetmn a l P the anentdevelo sanlnfecnon 7 b p p J 8 550 c PLhepanentdevelopsanlnfecnon 8 650 5738 d Pme patient develops anlnfectlon 7 8 650 812 e Pme patient develops anlnfeenon 7 5738 ANS C REF Seaman 5 2 AP 15 Suppose you wanuo estlmale me probabllllylhal a randomly seleaed customer at a a randomly seleaed waomerwlll pay by team card7 a o 2144 b 05le c o 7222 d o 8548 e o 8522 ANS A REF Secuon 5 2 AP 17 A m r d h me order m whlch me cards are dealt mere are 1598950 posslble nandsgt ofwhmh only 4 hands My ml 2 a um q What 15 me probablllly that a hand wlll be a royal u5h7 48 2 598 b 2 598 d 2598956 2 598m 9 4x52 2 598m ANS B REF Secuon 5 2 AP 12 A large cable wmpany reports that 70 of rts customers subsmbe to rts cable TV sermegt Use the grverr prebsbrmy mformauon to setert a hypothetical 100039 table Cable TV net CabIeTV Total Internet semee 50 170 not Internet servxce 550 130 680 Total 700 300 1000 b Cable TV net CabIeTV Total Internet servxce 170 250 420 not Internet servxce 30 550 580 200 800 1 000 Cable TV net Cable TV Total Internet servxce 350 70 520 not Internet servxce 450 130 580 Total 800 200 1000 El CabIETV netCabIeTV Total Internet servxee net Internet servxee 55 3 58 Total 80 20 100 CabIETV netCabIeTV Total Internet servxce 250 550 800 net Internet servxce 170 30 200 Total 420 580 1000 ANS A REF Section 5 3 A 19 r r one these students What rs the probabrhty that Luke 15 selected both of the nexttwo trrnes that the class rneetat a 0 00022 b 0 02222 c 0 5 d 0 01724 e 0 00015 Am A REF SecuonS 2 AP 20 A rental car wmpany offers two opuons when a car is rented A renter can choose to ent that gas 15 prepurchaaed eventthat a GPS rarented are rndependent wrth HA 0 25 and ms 0 50 r a n p tn rrarr prerpurchased and rows wn espondmglo whether or not a GPS is rented A not A Total 8 175 175 350 not B 325 325 650 Total 500 500 1000 not 325 325 650 Total 500 500 1 not 30 120 150 Total 200 800 1000 not 120 30 150 Total 800 200 1000 not 175 325 500 Total 350 650 1000 ANS E REF SecuonS 2 AP 21 whether the car purchased had a hybnd engme or he Not H bud and Phyhha male 3 75 Emu 025 029 067 088 b ANS B REF Semen 5 4 AP Letter Mailed To Nu Wash n D C 7 000 Use the gwen mformauon to estrmate the prohahrhty ofan oneume dehyery m New York a 405 6220 n 0 0651 b g n 0 7545 a 4330 N 0 0593 A 6550 N 0 0844 8 630 n 0 0667 ANS B REFt Section 5 7 AP SHORTANSW39ER 22 Some hmrtatrons othe c1assrca1 approach to prohahrhty were drscussed m the text Idenufy and hrreny drscrss m of these ANS 1 It only works when the outcomes are equally 111er 2 It cannot be used m ertam srtuatronsgt such as geometrrc prohahrhty 2 There 15 no way to wnven past experrence mto an expectatron aboutthe future REF Sectron 5 2 AP 24 t t t prohahrhty of a chance experrment REF Sectron 5 2 AP 15 therr rce cream The topprngs are classmed as erther candy c or hurt F topprngs Consrder the customers who order we cream a List all the events in the sample space b Using your sample space in part a list the outcomes for each of the following events A the event that both customers pick candy B the event that both customers pick the same type of topping C the event that at least one customer picks a candy topping A B C ANS a CC CF FC FF b A CC B CC FF C CC CF FC REF Section 52 AP 26 A small ferryboat transports vehicles from one island to another and the order the vehicles arrive will lead to slightly different placement on the ferry Consider the chance experiment where the type ofvehicle passenger P or recreational R vehicle is recorded for each of the next two vehicles that arrive at the dock a List all the events in the sample space b Using your sample space in part a list the outcomes for each of the following events A the event that both vehicles are passenger cars B the event that both vehicles are of the same type C the event that there is at least one passenger car A B C ANS a PP PR RP RR b A PP B PP RR C PP PR RP REF Section 52 AP 561 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 27 In a few sentences de ne the following terms a Sample space b Mutually exclusive ANS a The collection of all possible outcomes ofa chance experiment b Two events that have no outcomes in common REF Section 53 AP 28 As every Girl Scout knows statistics teachers seriously love Girl Scout Cookies The number ofboxes of GS cookies statistics teachers order like all important decisions made by statistics teachers is determined by independent rolls ofa 4 sided fair die lfa one appears 6 boxes are ordered if any other number appears 2 boxes are ordered a What is the probability that a statistics teacher places an order for 2 boxes of Girl Scout cookies b What is the probability that with two independently chosen statistics teachers will each order 6 boxes each c What is the probability that for two independently chosen statistics teachers the rst will order 6 boxes and the second will order 2 boxes d What is the probability that for two independently chosen statistics teachers exactly will order 6 boxes ANS a 3 b i 16 c i 16 d i 16 REF Section 53 AP 29 Suppose that 70 of the orders on a particular website are shipped to the person who is making the order and the remaining 30 are shipped to people other than the person placing the order Gift wrapping is requested for 60 of the orders being shipped to other people but for only 10 of orders shipped to the person making the order 562 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessib1e website in whole or in pan a What is the probability that a randomly selected order will be gift wrapped and sent to another person b What is the probability that a randomly selected order will be gift wrapped C Is gift wrapping independent of the destination of the gift Justify your response statistically ANS a 18 b 25 c No this can bejustifled in a number ofways For example if they were independent then Pgift wrapped Pgift wrapped l shipped to another person However 25 7 6 so they are not independent REF Section 53 AP 30 Consider the chance experiment in which a high school principal selects a sports event at random to attend The sex of the participants Male or Female is noted as well as the type of event Wrestling Volleyball Basketball or Swimming Let M be the event that the participants are male and B be the event that a ball is involved ie basketball or volleyball a What outcomes are in BC b What outcomes are in MU B c What outcomes are in Mn 3 ANS a MW MS FW FW b MW Mv MB MS FB FS c MV MB PTS 1 REF Section 53 AP MSC Section 53 31 A statistics class conducts a chance experiment in which they observe students who buy a snack and the school vending machines The type of food Liquid or Solid is noted as well as the number of calories of fat content 25 50 or 75 Let L be the event that the item is liquid and B be the event that the item has fewer than 75 calories of fat a What outcomes are in BC b What outcomes are in L k B 563 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part c What outcomes are in L n B ANS a L75 S75 b L25 L50 L75 S25 S50 c L25 L50 REF Section 53 AP 32 In order to ensure the safety of school classrooms the local Fire Marshall does an inspection at Thomas Jefferson High School every month looking for faulty wiring overloaded circuits etc At TJHS the new Academic Wing has 5 math rooms 10 science rooms and 10 English rooms The science rooms are divided into 8 biology and 2 chemistry rooms Each month the Fire Marshall randomly picks one of the rooms in the new wing to inspect each month Define the following events S the event the selected room is a science room B the event the selected room is a biology room M the event the selected room is a math room E the event the selected room is an English room C the event the selected room is a chemistry room Calculate the probabilities of the events described below 81 PS b PM or E c PE or B d PS and not C ANS a E 25 b E 25 c E 25 d A 25 REF Section 53 AP 564 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part probabllltles requested below A the event the selected employee has been wth the rm less than 5 years B the event the selected employee has been wrth the rm 5 gr 10 years c the event the selected employee has been wrth the rm over 10 years a PA b we c PA or B d PA and c ANS 3gt L ZSEI b E ZSEI 0gt E ZSEI d ZSEI REF Sectlons 2 AP 24 Students ln two classes ofupperelevel mathematlcs were classltled accordrng to class standrng and gendergt resultlng ln the followlng table Distributinn nf Studmtx Advulud math A the event that the selected student 15 a temale B the event that the selected student 15 a male c the event that the selected student 15 a senlor In the following table indicate by putting an X in the appropriate cells which is true for each pair of events X Yes Blank N0 REF Section 53 AP 35 In a few sentences explain the difference between conditional probability and ordinary unconditional probability ANS When we calculate a conditional probability we use information about events that have already occurred This is not true with ordinary probability REF Section 54 AP 36 Experimental studies utilize blinding to prevent researchers from biasing their measurements of the patients But can they guess the treatment In a study of a psychotherapeutic intervention clinicians who were blinded were asked to guess what treatment their patients received Data from that experiment are shown below Assume that these data are indicative of the population of these treatments Frequencies for Blinding Experiment Correct Incorrect I Guess Guess Eherapv 30 6 lacebo 26 l l a What is the probability that a correct guess is made for a randomly chosen subject b If a randomly chosen subject received the placebo what is the probability that the researcher correctly guesses the treatment 566 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part ANS a E 3 b E 37 REF Section 54 AP 37 The basketball team at North Snowshoe High is in a little bit of trouble Two of their players have just fouled out on technicals and due to the u the coach only has 4 players to choose from three forwards and a guard who doubles as the team statistician In his haste the coach will randomly choose two of the four to go into the game and of course will do so without replacement What is the probability that the team statistician will be selected ANS DNILJ REF Section 54 AP 38 The football team at North Snowshoe High is in a little bit oftrouble Two of their players havejust left the game with injuries and due to the u the coach only has 5 players to choose from three linemen a quarterback and the punter who doubles as the team statistician The coach must choose two of those five to go into the game Unfortunately it is snowing very severely making it dif cult for the coach to see the players on the bench Therefore he randomly selects two players to go into the game He CAN tell there are two players so of course he sends them in without replacement What is the probability that the team statistician will be selected be V3 1 Ct REF Section 54 AP 39 Investigators recently reported the results a study designed to assess whether or not the herb St John39s Wort is effective in treating moderately severe cases of depression The study involved 338 subjects randomly assigned to receive one of three treatments St John39s Wort Zoloft or a placebo The authors were primarily interested in whether St John39s Wort performed better than placebo and included Zoloft as a Hway to measure how sensitive the trial was to detecting antidepressant effects Their results are presented in the table below Response of Subjects vs Treatment 567 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part a What is the probability that a randomly selected subject had no response b What is the probability that a randomly selected subject was treated with Zoloft and had a full response c What is the probability that a randomly selected subject had a full or partial response given that they were treated with St John39s Wort d What is the probability that a randomly selected subject that didn39t have a full response was treated with Placebo ANS a 568 b 080 c 381 d 320 REF Section 54 AP Exhibit 51 In a survey of airline travelers subjects were observed in the coach section of airplanes to determine if men or women are bothered by a seatmate of the opposite gender using the common armrest quotPassengers who were asleep or lovers cuddled together were not counted since these were considered confounding circumstances The table below contains data gathered in that study Discontentment Felt When Seatmate Used Common Armrest Males and Females I I Bothered I Not bothered I Females 19 26 Males 38 18 Suppose one of these passengers was randomly selected Use the information in the table to answer the questions below In showing your work de ne and use appropriate notation 40 Refer to Exhibit 5 1 a What is the probability that the passenger is female b What is the probability that the passenger is female or bothered c What is the probability that the passenger is male and not bothered 568 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part a 7 1m 3 L 1m 0 18 REF Semen 5 4 AP 41 In due study m Exhxbxt 571gt passengers were also classmadby age Discnntumnmt m W39hm Sunms Uxul Cnllllnl Arman Male and kinda by Ag a The passenger 15 undemogt gweh that she 15 male b The passenger was bothered gweh that me passenger was over 40 c The passenger was male and over 40 ANS a a 45 b g 52 c 31 REF Semen 5 4 AP 42 In November 2002 Janet Napolitano a Democrat was elected Governor of Arizona defeating Republican Matt Salmon and Independent Richard Mahoney This was a somewhat surprising outcome since there are more registered Republicans than Democrats in the state The table below presents the results ofa sample of voters in the election The number who voted for each of the candidates is presented in the rows and the party af liation of the voters is presented in the columns Suppose that a voter is randomly chosen from these respondents Use the information in the table to answer the questions below In showing your work de ne and use appropriate notation a What is the probability that a randomly chosen voter voted for Napolitano b What is the probability that a randomly chosen voter is a registered Democrat c What is the probability that a randomly chosen voter cast a vote for Napolitano given that the selected voter is a Democrat d Commenting on this election A local reporter said HNapolitano won because she attracted a larger share of crossover voters A crossover voter is de ned as one who votes differently than his or her party af liation What is the probability that a randomly chosen voter cast a vote for Napolitano given that he or she is a crossover voter ANS a 47 b 36 c 852 d 544 REF Section 54 AP 43 Experimental studies utilize blinding to prevent researchers from biasing their measurements of the patients But can they guess the treatment In a study of a drug intervention clinicians who were quotblindedquot were asked to guess what treatment their patients received Data from that experiment are shown below Assume that these data are indicative of the population of these treatments Frequencies for Blinding Experiment Drug Standard treatment Incorrect Guess I 6 Correct Guess 32 570 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part a lf a subject 15 selected at randomgt what ls the probabllltythatthe researcher correctly guesses the Lrea39menW the researcher correctly guesses the treatmentv ANS a 55 73 e n 753 b 32 38 e n 842 REF Sectlon 5 4 AP 44 a m w w level ofcurloslty These charactenstlcs wlllsometlmes get them lnto trouble when they travel Lhmugh humaneuse areas such as parks When they become nulsancesgl the Park Servlce Park over a loyear perlod are glven m the table below Transplantzd Bur Tabla a an Kllled outside of ark a p m At be male and a nulsance in another area b p m At be female or successfully transplanted c p m At return to the capture area lfshe 15 a female d They bears are females If a randomly selected bear is observed to be a male w ls the probablllty rt wlll be a nulsanoe 7 a 14 153 3 E 153 a 7n d 2215 REF Sectroh 5 4 AP 45 An Austrahah shakegt the dramohd pythongt 15 about 2 feet long as an adult In a study othe t a and habrtat The other category mcludes treesgt logsgt rocks open goundgt and under mtermg cover shrubs Diamond Python Habitt seasohs Camuate the estrmated probabrhty that a m t t b spnng orsummer c A randomly seleaed dramohd back 15 observed m a buddmg or m the summer a 012 b 921 025 REF Sectroh 5 4 AP 46 At Thomas Jefferson High School students are heavily involved in extra curricular activities Suppose that a student is selected at random from the students at this school Let the events A M and S be defined as follows with probabilities listed A student is active in the performing arts PA 020 M student is active in vocal or instrumental music PM 032 S student is active in sports PS 035 PAm f 013p1msj 007 PMSj 030 Calculate each of the following show your work i PCA IMD ii melonr iii POI 539 ANS i 5625 ii 34 iii 105 REF Section 55 AP 47 Three of the most common pets that people have are cats dogs and fish In fact many families have more than one type of pet and some have all three Suppose that a family is selected at random Define the following events with the probabilities given Note the sh and cats combination doesn t seem too popular F a family has at least one pet sh PF 020 D a family has at least one pet dog PD 032 C a family has at least one pet cat PC 035 PFr iD 01181007 C 007 PQDIC 030 Calculate each of the following show your work i POI ID ii PA k D iii PCn D ANS i 5625 ii 34 iii 105 REF Section 55 AP 573 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 48 In a special report HSpeed Demons in the Cedar Rapids IA Gazette reporters used a radar gun to check the speeds of motorists in two counties They were shocked I to discover that some motorists were driving at a speed greater than the posted limits They reported the following information Some Speeding data for cities in Linn and Johnson Counties Speed Cars Over Over City Limit Counted Limit Limit Cedar Rapids 25 241 233 967 Iowa City 35 292 124 425 Iowa City 20 203 203 1000 Marion 30 329 268 815 Coralv le 25 174 161 925 Suppose that one of these cars is selected at random Consider the following events F the event that a driver is in a Hfast lane speed limit above 25 mph S the event that a driver is speeding a The table below shows the possible combinations of F and S Calculate the probabilities that a randomly selected driver would be in each ofthe cells Speed Limit Speed Limit gt 25mph 25mph or less quotFquot quotnot Fquot Driver speeding Driver not speeding b From the information in part a calculate PFU c From the information in part a calculate PFS d From the information in part a calculate PS e These events are represented in a tree diagram below What is the probability that a randomly selected driver will Hfollow the branches to the X 574 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessib1e website in whole or in part Speeding Nnr siteeeiliilg Fe ANS a Spud Limit Spud Limit gt ZSmDh 25mph or 12 I I ourquot l Drivu Spuding 315 422 39 39 125 017 b 922 c 295 d i792 e 315 REF Section 5 5 AP 49 One method tor increasingsales otboxes otcereal is to suggest to children that they complete a set otsmall toys Suppose one ot a set ot tiye toys is put in everybox Using one strategy the company couldput a randomly selected toy in each box otcereal Then each toy the likely number ofboxes ot cereal needed to complete the set ot toys a To simulate this strategygt assigi digits to the toys thatWill result in the probability ot selection oteach toy to be 0 20 Toyl Digits Toyz Digits Toy z Digits Toy4 Digits Toy 5 Digits b where one rim continues until a complete set ot the 5 toys is acquired 0 digits to help explain your procedure d 61790 55300 05756 72765 96409 12531 35013 82853 73676 57890 99400 37754 42648 82425 36290 45467 71709 77558 00095 32863 29485 82226 Suppose that the cereal company decides to put the toys in the boxes with different probabilities Toy 1 will be put in 30 ofthe boxes Toys 2 and 3 will be put in 20 ofthe boxes and Toys 4 and 5 will be put in 15 ofthe boxes Assign digits to the toys that will simulate these probabilities Toy 1 Digits Toy 2 Digits Toy 3 Digits Toy 4 Digits Toy 5 Digits Perform 5 runs and use your results to estimate the probability that it would take more than 10 boxes to complete the set of5 toys You may mark on the digits to help explain your procedure 19223 95734 05756 28713 96409 12531 42544 82853 73676 47150 99400 37754 42648 82425 36290 45467 71709 77558 00095 32863 29485 82226 68417 35013 15529 72765 85089 57067 50211 47487 82739 57890 20807 81676 55300 94383 14893 60940 72024 17868 24943 61790 90656 87964 47140 29385 67067 15803 12589 52167 18568 23243 55770 90846 86664 ANS Note For simulation questions there are many different correct ways to assign digits In the answer key an answer will be given but it is just one of many possible correct answers a Toy 1 digits 0 1 Toy 2 digits Toy 3 digits 4 5 Toy 4 digits 6 7 Toy 5 digits 8 9 N w Starting in the upper left corner ofa random digit table I would look at single digits from 0 9 until I get at least 1 digit from 0 1 1 digit from 2 3 1 digit from 4 5 1 digit from 6 7 and 1 digit from 8 9 Then lwould count the number of digits I needed to look at to achieve this 6 toy 4 1 toy 1 7 extra toy 4 9 toy 5 0 extra toy 1 5 toy 3 5 extra toy 3 576 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessib1e website in whole or in part d 3 toy 2 Thus it took 8 cereal boxes to get the set of5 toys Toy 1 digits 00 29 Toy 2 digits 30 49 Toy 3 digits 50 69 Toy 4 digits 70 84 Toy 5 digits 85 99 Using the scheme from part d the first 5 trials gave the following results 9 12 7 6 9 1 Thus the probability that it takes more than 10 boxes is Rs 7 REF Section 57 AP 50 A man has five ties and each day chooses a tie at random to wear to work He is colorblind and is wife frequently complains that he wears the same tie two days in a row Your task is to design and conduct a simulation that could be used to estimate the probability that he wears the same tie two days in a row in a 5 day week a To simulate the rst strategy discussed above assign digits to the ties that will result in the probability of selection ofeach tie to be the same Tie l Digits Tie 2 Digits Tie 3 Digits Tie 4 Digits Tie 5 Digits b Describe how you would use a random digit table to conduct one run of your simulation c Using the following lines from a random number table conduct 5 runs and estimate the probability that he wears the same tie two days in a row in a 5 day week Mark on the digits to help explain your procedure 37754 42648 82425 36290 45467 71709 77558 00095 32863 29485 82226 68417 35013 15529 72765 85089 57067 50211 47487 82739 57890 20807 ANS a Tie 1 digits O l Tie 2 digits 2 3 Tie 3 digits 4 5 Tie 4 digits 6 7 Tie 5 digits 8 9 b Starting in the upper left corner ofa random digit table Twould look at a set of5 random digits label each digit as tie 1 5 and look to see if there were any 2 adjacent digits with the 577 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part same tie If there are this represents a week where the man wears the same tie 2 days in a row c First week 3 tie 2 7 tie 4 7 tie 4 5 tie 3 4 tie 3 Thus in the first week he wears the same tie two days in a row actually twice Second week ties 32435 did not wear the same tie two days in a row Third week ties 52323 did not wear the same tie two days in a row Fourth week ties 24251 did not wear the same tie two days in a row Fifth week ties 533344 did wear the same tie two days in a row 1 Thus the probability that he wears the same tie two days in a row REF Section 57 AP 51 In a particular city 45 of donors have type 0 blood On a certain day the blood bank needed 4 donors with type 0 blood to restock their reserves The director has the option of waiting to get 4 donors during the day or ordering type 0 blood from a neighboring blood bank The director would like to replace the blood before 12 donors come to the bank the typical number to arrive before noon Your task is to design and conduct a simulation to estimate the probability it takes 12 or more donors to get 4 with type 0 blood a To simulate the arrival of blood donors from this population assign digits to the blood types that will result in a probability of success Type O donor of 045 Type O Digits Other than Type O Digits b Describe how you would use a random digit table to conduct one run of your simulation c Using the following lines from a random digit table perform 5 runs Based on your results what do you estimate to be the probability of getting 4 Type O donors before 12 donors arrive at the blood bank Mark on the digits to help explain your procedure 68417 35013 15529 72765 85089 57067 50211 47487 82739 57890 20807 81676 55300 94383 14893 60940 72024 17868 24943 61790 90656 87964 73311 12190 06628 71683 12285 39814 29103 81733 73035 57446 99209 578 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessib1e website in whole or in part ANS a Type 0 digits 00 44 Other than Type 0 digits 45 99 b Starting in the upper left corner ofa random digit table lwill look at pairs of random digits from 00 99 until I get 4 numbers from 00 44 Then Twill count the total number of two digit numbers I looked at to determine the number of blood donors needed c First run 68 other than Type O 41 Type O 73 other than Type O 50 other than Type O 13 Type O 15 Type O 52 other than Type O 97 other than Type O 27 Type 0 Thus on the rst trial it took 9 donors to nd 4 of Type 0 Second run 17 donors Third run 8 donors Fourth run 6 donors Fifth run 8 donors 4 Thus the probability that it takes fewer than 12 donors to get 4 onype O 58 E REF Section 57 AP 579 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part Chapter 06 Random TRUEFALSE 1 A random vanable 15 dwcrete 11 dne value othe random vanable depends upon dne wome ofa chance expenmenl ANS F REF Secuon 5 1 AF on the number 11ne ANS T REF Secuon 5 1 AF 2 The drsmbuuon of a11va1ues of a randomvanable 1s called a norrna1 d15mbul1onr ANS F REF Secuon 5 2 AF For a conunuous random var1a1a1ergt 1he hergnc othe densuy mrve over an 1n1erva1 a to b represean 1he probabmty than 1s between a and b ANS F REF Semen 5 2 AF 5 For every random vanah1egt Pa s x s b e Pa lt x lt 5 ANS F REF Semen 5 2 AF 5 Fora dwcrele nndom varrahlexgt Ax 2x p0 mma ANS T REF Semen 5 4 AF 7 For a dwcrele nndom varramegt ax e 2 rue MK mma ANS F REF Secuon 5 4 AF 139 2 1m 1s a random var1a1a1egt and randomvanable 1 1s de ned as ro11owsgt y a bnvhen w b x ANS F REF Secuon 5 4 AF 9 For random vanablesm and ygt 1fy 11 bx 1hen a a 5er ANS F REF Secuon 5 4 AF 10 lfrandom varlables n and x are lndependentgt then uf W ANs T REF Sectlon 5 4 AF ll The standard normal dlstrlbutlon has a mean otl and standard devratlon om ANS F REF Sectlon 5 5 AF 15 no obvlous pattern m the scatter otpolnts ANs F REF Sectlon 5 7 AF MULTIPLE CHOICE 13 Whlch of the followlng randomvarlables are dlstretev l the volume ofa balloon ln llters c lllonly d llandlllonly LILandm ANs D REF Sectlon lAP l4 Whlch of the followlng random varlables are oontlnuousv I the alr pressure in an automoblle tlre ln pounds persquare lnch U the dlameter otan automoblle tlre ln oentlmete s In the number ofmlles traveled by an automoblle tlre a lonly b landlllonly ll and lll only d LILandIH e None otthevarlables 15 conllnuous ANS E REF Sectlon 5 1 AF 15 d 4 replacement Llst the possrble values for the followlng random vanable x number ofsllps marked 1 u l u l 2 a b 2 c ANS A REF Search 5 1 AF 15 Frepertreh of o 25 o 15 o 40 o 10 calls of tast yeasz graduates ohms umversrty What 15 PO 3 25 7 ANS E REF Search 5 2 AF 17 Supposer 15 a tehtrhueua random varrable wrth the probabrhty drstrrbutreh shouwn below 2H 4H Lin 8 1 U What probabrhty rs represented by the shaded areav a PI x lt m b PZEI x lt SE a lemn x lt5n d ma gt 5n e hehe enhese ANS E REF Search 5 2 AF 18 A chemical supply company currently has in stock 100 pounds ofa certain chemical which it sells to customers in 5 pound lots Let X the number oflots ordered by a randomly chosen customer The probability distribution of x is as follows x 2 3 4 5 p 01 04 02 03 Calculate the mean value of x a 22 b 25 c 27 d 33 e 37 ANS E REF Section 64 AP 19 Determine the area under the Z curve to the right of 7182 Pkg lennm5 Pk2d3 m PQZA8 U PbZ lamp09 PQZAB UM ANS D REF Section 66 AP ruin90 s 20 A gasoline tank for a certain car is designed to hold 19 gallons of gas Suppose that the random variable x actual capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean 190 gallons and standard deViation 02 gallon What is the probability that a randomly selected tank will hold at least 189 gallons a 019 b 069 c 1 d 031 e 081 ANS B REF Section 66 AP 21 Thirty seven percent of the customers of a grocery store use an express checkout Consider four randomly selected customers and let x denote the number among the four who use the express checkout Calculate PEx 5 2 a 053 b 085 c 070 d 030 e 050 ANS B REF Section 65 AP 583 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 22 A business has five customer service telephone lines Let x denote the number oflines in use at any given time Suppose that the probability distribution of x is as follows x 0 1 2 3 4 5 px 010 020 035 015 015 005 Find the standard deviation of x Round your answer to two decimal places a 25 b 133 c 098 d 122 e 125 ANS B REF Section 64 AP SHORT ANSWER 23 What is a random variable ANS A random variable is a numerical variable whose value is the outcome of a chance experiment REF Section 61 AP 24 Using the notation C continuous and D discrete indicate whether each of the random variables are discrete or continuous a The number of defective lights in your school39s main hallway b The barometric pressure at midnight c The number ofstaples left in a stapler d The number ofsentences in a short story e The average oven temperature during the cooking of a turkey 1 The number of lightning strikes during a thunderstorm ANS a D b C c D d D e C 139 D REF Section 61 AP 584 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 25 Using the notation C continuous and D discrete indicate whether each of the random variables are discrete or continuous a The number of stair steps to the principal39s of ce b The average night time temperature in July at the top of Long39s Peak in Colorado c The number offorks in your kitchen d The number of sentences in a short story e The circumference of a California redwood tree f The number of grains of sand it takes to fill a quartjar ANS a D b C c D d D e C f D REF Section 6 AP 26 From your own experience give an example of a continuous random variable and a discrete random variable In a few sentences explain why each is categorized as continuous or discrete ANS Examples will vary Explanation for continuous random variable must include the idea of an interval of values on a number line Explanation for discrete random variable must include the idea of isolated values on a number line REF Section 61 AP 27 At the College of Warm amp Fuzzy good grades in math are very easy to come by The grade distribution is given in the table below Grade A B c D F Proportion 030 035 025 009 001 Suppose three students are to be selected at random As each is selected their math grades are written down and they are replaced back into the population of students Three possible outcomes of this experiment are listed below Calculate the probabilities of these sequences appearing a BAC b CFF 585 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated oi postedto a publicly accessible website in whole 01 in part c ABA ANS a PBAC PB PA PC 353025 002625 b PCFF PC PF PF 250101 0000025 c PABA PA PB PA 303530 00315 REF Section 62 AP 28 At the University of Tough Love good grades in math are very hard to come by The grade distribution is shown in the table below Grade A B c D F Proportion 010 015 035 035 005 Suppose three students are to be selected at random As each is selected their math grades are written down and they are replaced back into the population of students Three possible outcomes of this experiment are listed below Calculate the probabilities of these sequences appearing a ABC b CCF c BBA ANS a PABC PA PB PC 10l535 000525 b PCCF PC PC PF 353505 0006125 c PBBA PB PB PA l51510 000225 REF Section 62 AP 29 Fifty five percent of the students at Thomas Jefferson High School use Hlunch cards to charge their lunch rather than bringing money to school Assuming that the method of payment cash or lunch card for one student is independent of the method of payment for the next student in line what is the probability of observing the following sequence for the first five students through the lunch line Cash Card Cash Card Cash ANS PCash Card Cash Card Cash 4555455545 00276 REF Section 62 AP 586 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated oi postedto a publicly accessible website in whole 01 in part 30 One common method used to forecast the results of elections is to take an Hexit poll asking people who they supported as they come out of the voting place Suppose Smith and Jones are running for City Dogcatcher ln point of fact 60 of the voting public in the neighborhood of the polling place support Smith Assuming that the candidate of choice for a voter leaving the polling place is independent of the candidate of choice for the next person to leave what is the probability that the rst 5 voters to leave the polling place would have this sequence for candidate of choice Smith Smith Smith Jones Smith ANS PSmithSmithSmithJonesSmith 66646 005184 REF Section 62 AP 31 In a major study by the statistics classes at Washington High School city parking spaces were examined for compliance with the requirement to put money in the parking meters Overall the students found that 76 of metered parking places had meters that had not expired and 24 had meters that were expired If the traffic of cer in charge of ticketing cars with expired meters checks meters at random what is the probability he or she will nd an expired meter before the 3rd one ANS Pexpired before 3 1 7 P1st not expired and 2nd not expired 1 7 0762 4224 REF Section 62 AP 32 In a major study by the statistics classes at Jefferson High School parking spaces were examined for compliance with the requirement to put money in the meters Overall the students found that 80 of metered parking places had meters that had not expired and 20 had expired If the traf c of cer in charge of ticketing cars with expired meters and starts at a random location in the City what is the probability he or she will nd an expired meter before the 3rd one ANS Pexpired before 3 1 7 P1st not expired and 2nd not expired 1 7 0802 036 REF Section 62 AP 33 During World War II The German forces launched ying bombs missiles against London In a study of the effectiveness of these ying bombs a researcher divided the south of London into 575 squares of area equal to 025 square km and counted the number of these squares that had sustained exactly khits The data for 0 4 hits in an area is given in the table below k FlyingBomb Number squares hits 39 39 khits 0 229 1 211 2 93 3 35 4 7 587 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessib1e website in whole or in part London a F111 m are table below mm are esumated probabrmy dxsmbuuon errgt and sketch a probabrmy hrsmgam for r Probabrmy drsmbuuerr Auntie rhmm h arm Usrng your asumated probabrmres m pan agt esumace me followmg i u m 1gt me probabrmy that 1 ymg bomb hxt m a randomly seleaed square m lt 2 me probabrmy that fewer mar z ymgbombs hm m m 2 zgt me pmbabrmy that at least 2 ymg bombs hxt ANS a Probabrmy Drsmbuuen Hrsmgam x m u mayo 927 m my 0720 REF Secuon ZAP 24 nr h nFqurA q q counter 15 gwm m the table below N and nf llu cm withk u 39du k Dar dzx o NN mmmN Nuwwu Lenhe random vanablex number ofpamcles counted m a 7 5 sewnd ume pened a Fxll m me table below mm me esumated probabxmy dxsmbuuon g and sketch a probability histogam for x Pmbabxmy dmmmn Probabxhty histogam b Uslng the estlmated probabllltles in part agt estlrnate the followlng l m lgt the probablllty that l pamcle was counted in 7 5 sewnds u m lt zgt the probablllty that fewer than 2 pamcles were counted ul m2 zgt the probablllty that at least 2 pamcles were counted ANS a Probablllty Dlsmbullon t lstogarn Number ofpamcles l m u m lt z m m 2 z REF Settlon 5 2 AP 25 The denslty curve for a wntlnuous randorn vanable 15 shown below Use tlus mrve to flnd the followlng probabllltles a m lt l b m lt x lt z t m 15 at least 2 10 20 30 41 You may use the followmg area formulas m your calwlauons Area orareaangle A tw Areaofau39apezmd Ahb bz Areaorangmmmgle A gab ANS a areaofu39apezmd Pxltll c REF Secuon 5 2 AP 25 The dmsny curve for a wnunuous random vamble 15 shown below Use ths mm to nd the followmg probabumes a m lt 1 b m lt x lt z c m 15 at least 2 10 20 30 40 You may use me followxng area formulas m your calwlauons Area ofa reaangle A 7 2w Areaofau39apemxd mb bz Area ofa nghl mangle A ab ANS 3 z areaofmangle ma 1mg b areaofu39apezmd pa x ltz1 3 c areaofmanglePx23 gag uzs REF Semen 5 2 AP QVQ from o mmuzes m 20 mmuzes a Sketch the probabxmy distribution ofT mung forGOD 017 ANS a Dewy mm 15 a rectanglegt 1amp1th 20gt hexght o 05 at le below nna nna b FTgt 7 120 05 o as Illustrated at 11311 above REF Semen 5 2 AP 32 QVQ minutes to z o mmuzes a Sketch the probability distribution ofT for GOVD o 17 ANS a Dewy mm 15 a rectangle 1amp1th 20he1l 120 alle below b PTgt 12 18 u an Illustrated mm above REF Semen 5 2 AP 29 random vanable prov1de7 ANs The mean of a randomvanable 15 1he longelerm average ermanygt many ma1a The standard ma1a REF Semen 5 4 AF 40 standard devrauon onhrs dmnbuuom ma 015 mm ANS 14 Zr pxll 151n zszn4n3n 211 1 as 28 W e1 552015e0 5520 25 0 2321 40 1 2321 20 5 REF Semen 54 AF 41 At a 1arge un1vers1ty students have enher a hna1 exam or a hna1 paper at 1he end ofa course The table below 11515 1he d15mbut1on of 1he number of hna1 exam that smdema at 1he unwersny 11 1 1 nhrs d15Lnbul1on7 2 mm AN 5 u 2x W e um n5 111 zs 211 410 311 3n195 UHF pltxgt e1 9321 05 e0 9321 25 0 0321 40 1 0321 20 m 1747s o 2545 REF Semen 5 4 AF 42 to the followlng probablllty dlstnlyutlon 100 Conslder the random varlable x dollar amount ln rent collected m a Monopoly roll varlable x7 b If the probabllltles are assoclated wth the outcomes as m the table abovegt what ls the standard devratlon othe random vanable ANS a ux Zx m 27d a Zaw Pltxgt am REF Sectlon 54 AP Wu 42 Whlle playmg Monopolygt Laura estlmated the probabllltles ofthenonrzem rents accordlng to the followlng probablllty dlsu39lbullon mo Conslder the random varlable x dollar amount ln rent ln a Monopoly roll varlable x7 b If the probabllltles are assoclated wth the outcomes as ln the table abovegt what ls the standard devratlon othe random vanable AN S a we 2x new REF Sectlon 5 4 AP 44 u m t m m t December has a mean of l7 Celslus Wlth a standard dewatlon of 2 Celslus Let Fbe the random vanable maxlmum dally temperature in degees Fahrenhelt Degrees F g 0 32 a What 15 the mean ofF7 b What 15 the standard devlallon ofF7 ANS a ucezzedzw b HFUCKZ gagesw REF Sectlon 54 AP 45 When dnvlng the natlon s hlghways Anna 15 lmown as somethlng of a lead root The devlallon on mph Unfortunatelygt the state m whlch she goes to wilege adjusts the nes so that the amount othe me 15 glven by the formula F10MFH llzgt where F15 the amount of the hnegt and Mills the number ormlles overthe speed llmlt Let random vanable Fbe the amount of her flne lfshe 15 randomly stopped for speedlng a What 15 the mean ofF7 b What 15 the standard devratlon ofF7 ANS a uFuIEMIPHHZl uwallz3187 b aFalWPHllz1nawn2u REF Sectlon64AP 45 ttnt randomly guessed on all the questlons 3 chance experlment Wlth prohahlllty ofsucoess equalto o 50 lrwe de ne the random random student who 15 guessmg7 blnomlal chance expenmentwlth probablllty ofsucoess equal to o 10 lrwe de ne the Mfor a random student who 15 guesslng7 c n ttl na at tn man and standard deylatlon of the random vanable m d essrng on the multlple cholce part ofthe testgt what 15 the ect 15 the 4th multlple cholce If a student 15 randomly gu probablllty thatthe rst multlple cholce questlon corr quesllor ANS a mean truefalse u e n 7 sum 5 e 25 standard deylatlon truefalse a e n quotI e r sum sn s e 1 sad b mean multlple cholce M e n r nn z e a standard deylatlon multlple cholce UM n me 7 4m zn a e 2 5m c mean totalscore um e um 2M e u 2 e 25 2a e 41 st deyratron total score an 9 Ma a e lz 54 4 0 RM 2 381 l73 m4 d F rst mlssed 15 4th m wrongFcmrecl REF Sectlon 5 5 AP 47 learn to slu On Blg Bunny slope slclers Wlll fall to malce the turn at Blg Bend On thtle Bunny sl egt t t t a m apart that they dont run lnto each othergt so thelrspllls are all rndependent 3 slclers needlng to be dnvm to the Flrst Ald Statlon from Blg Bendgt we can model th5 b w t m a standard deylatlon ofL7 0 calwlatlng B L What are the mean and standard deylatlon of the random vanable 27 d e 15 slclers are sent down from the top ofBlg Bunny slopegt they are sent one at a e to be When th trme What 15 the probablllty that the rst one needlng the Ambulance 15 the 7th on sent down the 5101397 597 ANS a me E hr an n 7r253 e75 standarddevratronB HI m min zs37s 5252291 b meanL uln rzs1zs standarddevratronL sf n men zs19 es 22515 c meanBL uh hlehlenezs 1n st devratronBL a dung s szszz Mam d F rst fall 15 7 m OK Ffall 0 We 2 o 0252 REF Sectron 5 5 AP 42 Inspemng meat 15 a very rmportant part ofthe process orfnsurrng healthy food So that comes up a4gt a sample rstahen ofthatmea tu Fortysrdes ofbeefare avadahle for possrhle Xira lequot a What 15 the mean othe random varrahle x7 b What 15 the standard devratron onhe random varrable x7 ANS a mean hx nrr4 25 1n b standarddevxauon ax who r REF Sectron 5 5 AP 49 t t h a N t V a m xrrtoomesupaA chrps purchased out one a What 15 the mean othe random varrahle x7 b What 15 the standard devratron orthe random varrabte x7 ANS a mean up e M 4U 25 e In b standard devlauon up mule r e z 739 REF Sectlon 5 5 AP 50 At the last home football gamegt the senlor football players wallc through a speclally h a mu lnches of a randomly selected padded toothallplayer 3 t l l tn h 2 54 centlmeters and we de ne random vanable m wldth m centlmeters of a randomly selected padded football player What are the mean and standard deylatlon ofm 7 b n n r ml m players What are the mean and standard devratlon om 0 players lsspeclnedsothatthe football players have roomto avold each other Thls leads to r xggl mom would change the mean and standard deylatlon in part b Do notrecalculate the mean and standard devratlon z 54w 2 54 7d 2m 52 54w 7 545 7 7m b utz new av 44easz527w an would mcrease by 10 to 70 c The me The standard devratlon would remam unchanged 7 07 REF Sectlon 55 AP 51 mm h t gtllwasof charlothltchlng purposesgt the wldest measure across a horse ocmrs m the rump area The mean wldth m lnches across the rump of a randomly seleded horse to 4 De ne random vanable h wldth m hands amass the rump of a randomly selemed horse What are the mean and standard devratlon 0M7 b Suppose horses are randomly chasm for a pamwlar Roman ohanol De ne random vanable c hr hz to be the rump wldth ortworandomly selemed horses What are the mean and standard devratlon om standard devlatlon ln part b Do Lotreealnrlate the mean and standard devratron ANS a ll llw4law4 mstmnd 4Hw4Shami b u 2 m 54 a 44522222w t The mean would morease by l5 lnohas to 54 The standard devratlon would be unchanged 2 22 REF Settlon 5 5 AP 52 Deterrnrne the followlng areas under the standard normal 2 mrve a The area underthe 2 curve to the le on 52 b The area underthe 2 curve to the le orel 22 t The area underthe 2 curve to the nghl om 75 d The areaunderthezcurvetotherrgntorel 47 e The area underthezturvehetweenel and 2 t The area underthe 2 curve between 72 5 and el 2 ANS a o 9942 b o 0918 t 02225 d o 9292 e o 2400 l o 1104 REF Sectlon 5 5A 53 Determine the following areas under the standard normal 2 curve a The area under the 2 curve to the left of l 56 b The area under the 2 curve to the left of72l3 c The area under the 2 curve to the right of 088 d The area under the 2 curve to the right off 23 e The area under the 2 curve between 72 and 3 f The area under the 2 curve between 724 and 714 ANS a 09406 b 00166 c 018 94 d 08907 e 09759 f 00726 REF Section 66 AP 54 For a variable that has a standard normal distribution a What is the probability that z lt 7134 b What is the probability that z lt 256 c What is the probability that z is between 715 and 15 d What value of Z separates the smaller 5 of the standard normal distribution from the larger 95 e What values of 72 and 2 separate the middle 90 of the standard normal distribution from the extreme 10 ANS a 00901 b 09948 c 08664 d z 71645 e 271645 tozl645 REF Section 66 AP 601 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 55 For a variable Z that has a standard normal distribution a What is the probability that Z lt 7245 b What is the probability thatZ lt 167 C What is the probability thatZ is between 7143 and 143 d What value of Z separates the smaller 10 of the standard normal distribution from the larger 90 e What values of 7Z and Z separate the middle 95 of the standard normal distribution from the extreme 5 ANS a 00071 b 09525 c 08473 d Z 71 282 6 27196010Z1960 REF Section 66 AP 56 Let Z denote a random variable having a standard normal distribution Determine each of the following probabilities a PZ lt 128 b PZ lt 7105 C PZ gt 7251 d P7130ltZlt 154 ANS a 08997 b 01469 c 09940 d 08414 REF Section 66 AP 57 Let Z denote a random variable having a standard normal distribution Determine each of the following probabilities 3 b C d PZlt 136 PZlt7205 PZgt7115 137110 ltzlt 254 602 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part b omoz c o 2749 d o 2522 REF Semen 5 5 AP 52 m t u ANs Pz lt4 5 n 2552 PXlt117Pzltlz REF Sectmn 55 AP 59 The owners onhe Burger Eanperrurn are lookmg for new suppher of omens for therr t h t h h tt a a t t channeters between 9 and 10 cm Company A prevrdes omens wrth channeters that are usab1e onmns7 yustrry your choice wrth an apprupnate stausueal argument ANs The omens from Company A wru be between 9 and 10 cm channeter wrth prebabrhty P9ltdltmP Jeweln23ltzltezsnzazn 9 and 10 cm charneter wrth prebabrhty The omens from Company B wru be between P9ltdltl lt ltWJJG1W2lt2lt45022142 p REF Semen 5 5 AP t h h tt a careful analysrsgt apprexunatelynerrnauy drstrrbuted wrth rnean 10 5 m and standard devratren of 1 1 m usable ternateesv Justrry your home wrth an apprepnate statrsueal argument n ANS The omens from Company A wlll be between 9 and 10 m cllameter Wth probablllty P5 ltd lt1UP lt lt Pel 3535 lt2 4545 n 2384 The omens from Company B wlll be between 9 and 10 cm cllameter Wth probablllty P5 ltd lt1UP lt2 Quaiy39z Pel 525 lt2 375 n 3U17 REF Sectlon 5 5 AP 51 Z40m5 a A l t m mean reactlon tlme for le ehanders ln thls dlstnbutlon b About what pmpomon ofnghvhanders reacllon tlmes would be better l e smaller than the mean readlon tlme for le ehander ANS 3 of the dlstnbutlon should be at 21 ogt and the lnnettlonpolnts at 170 and 150 mean otlemtanuets b ml lt M Fzlt o 75 o 7724 REF Sectlon 5 5 AP 210ms 3 reattlon tlme fornghtehanders ln ths dtstrlhutlon b bout wh tpropomon of le ehanders reacllon llmas would be better l e smaller than de A a the mean reattlon Mme for rlghlehan 5 7 ANS 3 of the dtstrlbutlon should be at 24 ogt and the lnnettlon polnts at 202 and 272 menu alllljhx lmlulel mu m b PL wk Pz lte 9375 n 1743 REF Sectlon 5 5 AP 52 The tlmethat nukes arandornlyselected employeeto perform a certalntask 15 20 seconds The slowest 10 that lsgt the 10 wth the longest llmes are to be glven remedul Lralnlng Whattlmes quallfy for the remedlalu39almng7 ANS xelzu llmes Pzgtznlnzlza Solve m gt128 ogetxgtl455 REF Sectlon 5 5 AP 54 reason for your shame Jk m Vocabulary Score Math Concepts Score ANS shows a malghl lme The plot ofVocabulary Swre shows a cllsuna S shapegt lndlcallng me dlsu lbullon ls not normal REF Semen 5 7 AF 55 Bne y desmbe now one would declde whloh onwo lransrormauons was better for Ll39ansformlng skewed data to oblaln a cllsmlmuon Lhalwas approxlmalely normal ANS one for wnlm me normal probablllly plot ls has more of a stnlghlrllne pattern REF Semen 5 7AF 55 Bne y desmbe now me correlallon coefflclenl can be used to check forummanly ANS q M m l reasonable to belleve that me underlylng cllsmlmuon ls approxlmalely normal REF Semen 5 7AF Chapter 07 An Overview of Statistical InferenceLearning from Data TRUEFALSE 1 Suppose researchers would like to determine the proportion of Americans who own dogs This would be a hypothesis testing problem ANS F REF Section 71 AP 2 When selecting an appropriate method for data analysis one important consideration is the number of and type of variables involved in the situation ANS T REF Section 72 AP 3 When selecting an appropriate method for data analysis the only important consideration is the number of and type of variables involved in the situation ANS F REF Section 73 AP MULTIPLE CHOICE 4 Consider the following two statistical inference situations I A technician at a water bottling facility wishes to test whether one of the lling machines is delivering less uid per bottle than it is intended to deliver ll Another technician at this same facility wished to determine the number of milliliters of water being delivered per bottle for the filling machine in question Which of these inference situations are hypothesis testing problems a I only b H only c both I and H d neither 1 nor H e Situations such as l and H are not suitable for statistical inference ANS A REF Section 71 AP 5 For which of the following experimental questions would you be most interested in the population proportion instead of the population mean At this university how many minutes a day do students exercise Do students at this university intend to seek work immediately after graduation Is the GPA of statistics students at this university higher than the national average What is the mean GPA of statistics students at this university Do students at this university score higher than the national average on the Graduate Record Examination GRE ANS B REF Section 72 AP 994165 607 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 6 For the described study below select the answers for the following key questions or Number of Samples A study was conducted to test an old adage that cats sleep more when the ambient temperature is higher In the study cats were isolated from distractions in areas of xed temperature and were videotaped The videotape footage was then reviewed to determine the percent of each 24 hour day spent asleep Three large groups of randomly selected cats were randomly assigned to one of three environmental temperatures Hypothesis Experimental data Univariate and numerical data One treatment Estimation Sample data Univariate and numerical One treatment Hypothesis Experimental data Bivariate and numerical data Three treatments Estimation Sample data Bivariate and categorical data Three treatments Estimation Experimental data Univariate and categorical Three samples ANS C REF Section 72 AP 990ch 7 In many areas of the US honey bee populations have been devastated in recent years and the cause is not yet well understood A researcher surveys a large sample of honeybee colonies and rates each hive as healthy or unhealthy What best describes the type of data collected in this study a univariate numerical data b bivariate numerical data c univariate categorical data d bivariate categorical data e none of these ANS C REF Section 72 AP 8 In many areas of the US honey bee populations have been devastated in recent years and the cause is not yet well understood The general opinion amongst the beekeepers in a particular region is that the problem is intensifying and a researcher sets out to settle this question by surveying the health of a large number of randomly selected hives Which of the following best describes this study hypothesis test with sample data a b estimation study with sample data c hypothesis test with experimental data 608 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part d estimation study with experimental data e All of these are good descriptions ANS A REF Section 72 AP 9 A technician wishes to examine the breaking pressures in pounds per square inch of three brands of adhesives In this study the adhesives are used to bond two identical squares of l2 thick pieces of acrylic plastic face on and then the assembly is tensionally stressed until the bond failsF or each of the adhesive brands the test is repeated for 50 trials How many treatments are involved in this study a 3 b l c 50 d 15 0 e 2 ANS A REF Section 72 AP SHORT ANSWER 10 Describe the difference between an estimation problem and a hypothesis testing problem ANS An estimation problem is one where we would like to learn something about characteristics of the population A hypothesis testing problem is one where we would like to decide if there is evidence to support some claim REF Section 71 AP ll Suppose a researcher is collecting data about the amount of soda Americans consume in one day If the researcher was to gather two separate representative samples from the population differences may exist between these samples These differences may be attributed to what ANS Sampling variability REF Section 71 AP 12 Suppose a researcher is collecting data about the amount of soda Americans consume in one day The researcher would like to determine if Americans consume over 12 ounces of soda per day on average What question type Q is this estimation or hypothesis testing ANS Hypothesis testing REF Section 72 AP 609 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 13 Suppose a researcher is collecting data to compare the average amount of soda consumed daily by men and women The researcher will ask participants to state the amount of soda they consumed on the previous day The researcher would like to determine if differences exist in the amount of soda consumed between the genders What variables are involved Also list the type of each variable ANS There are two variables Gender and Amount Consumed The variable Gender is categorical The variable Amount Consumed is numerical REF Section 72 AP 14 Suppose a researcher is collecting data to compare the average amount of soda consumed daily by men and women The researcher will ask participants to state the amount of soda they consumed on the previous day The researcher would like to determine if differences exist in the amount of soda consumed between the genders Is this an observational study or an experiment ANS This represents an observational study REF Section 72 AP 15 List the five step process that should be used in an estimation problem ANS The rst step is to explain what population characteristic you are estimating the second step is to select an appropriate method for estimation the third step is to check assumptions are met for the procedure the fourth step is the perform the necessary calculations and the fifth step is to communicate the results of the procedure REF Section 73 AP MSC Section 73 16 List the five step process that should be used in a hypothesis testing problem ANS The rst step is to define the hypotheses that will be tested the second step is to select an appropriate method for testing the third step is to check that assumptions for the procedure are met the fourth step is to perform the necessary calculations and the fifth step is to communicate the results of the procedure REF Section 73 AP 610 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part Chapter 08 Sampling Variability and Sampling Distributions TRUEFALSE l A statistic is a characteristic of the population ANS F REF Section 8 AP N E and p are statistics ANS T REF Section 81 AP 3 Jul and CI are statistics ANS F REF Section 82 AP 4 As It grows larger the mean of the sampling distribution of gets closer to u ANS F REF Section 82 AP 5 The standard deviation of the distribution of decreases as It increases ANS T REF Section 82 AP 6 The sampling distribution of tends to be more spread out for larger sample sizes than for smaller sample sizes ANS F REF Section 82 AP 7 The distribution of will always have the same shape as the distribution of the population being sampled ANS F REF Section 82 AP 8 The closerp is to 0 or 1 the larger It must be in order for the distribution of to be approximately normal ANS T REF Section 82 AP 9 Tip 090 a sample size ofn 10 is large enough for the sampling distribution to be well approximated by a normal distribution ANS F REF Section 82 AP 10 The mean of the sampling distribution of 3 isp no matter how large n is ANS T REF Section 82 AP 61 1 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 11 m A t m t drsvrrbutmn ANS T REF SecuonRZAP MULTIPLECHOICE 12 Whmh of the followmg symbols 1 used to 1nd1cate a populauon propomom a b c d e Mutvt u ANS A REF Semen 2 1 AF 12 Whmh of the followmg statements 15 a populauon propomom ate 06 reports that 54 of state s muzms own at 1east one dog of50 randomlyrseleaed 1ndmdua1sgt 19 1nd1caled that they more dunng sleep mean metrme ofall cellphone batterres 15 11 2 hours Ast b Out 0 The mean boot t1me was 22 sewnds earthese e ANS A REF Sectmn 2 1 AF p 5n Detenmne the mean and standard devmmn othe samplmg drstrrbutmn of 3 forms samp1es1ze n mu 5n standard devmuon av 85 standard devratmn a ANS A REF Sectmn 2 zAF 15 A samp11ng d15u391bul1on of 3 can be regarded as apprexrmate1y normal when what condmons are metv a n 2 3n 1 n 2 1n 0 np25andn1epj25 d n25 e npzlnandn epjzln ANS E REF Sectlon 2 ZAP 15 the standard devratlon of 3 be srnallestv a n40andp0z b n 50 and 0 4 c d e REE Sectlon 2 ZAP 17 Suppose that 2 ohm mstorners of a cable televlslon companywawh the Jewelry customers and to use 3 as an estlrnate othe populatlon proportlon Deterrnlne the standard devratlon of 3 0021 b 0005 2400 d 0070 0041 ANS A REF Sectlon 2 2 AP wlll use 3 the sample proportlongt to estlrnate p Deterrnlne the standard devratlon of 3 a 0005 b 0025 c 0 100 d 0042 e 0070 ANS E REF SectlonR ZAP 19 ln arandornsarnple of 79 students at aunlversltygt 7had the u Suppose you are lnterested 1n learnlng about the value om the proportlon of all students at thls unlverslty who have the u Thls prop lon can be estlrnated uslng the sarnple proportlongt 3 What 15 the value of 3 for thls sample7 a 0097 b 0250 c 0089 d 0081 e 0700 ANS C REF Section 83 AP 20 Some colleges now allow students to rent textbooks for a semester Suppose that 73 of all students enrolled at a particular college would rent textbooks if that option were available to them If the campus bookstore uses a random sample of size 40 to estimate the proportion of students at the college who would rent textbooks then what is the standard deviation of the sampling distribution of 5 a 0079 b 0177 c 0070 d 0031 e 0197 ANS C REF Section 83 AP SHORT ANSWER 21 What is a sampling distribution of a statistic ANS The distribution of the possible values of a statistic is called its sampling distribution Note Generally if the student communicates the idea that the sampling distribution associates different values of the statistic with their probabilities he or she should get credit REF Section 8 AP 22 The principal at John F Kennedy High School has been asked to provide the average number of classes taken by the students at KHS Since the computer system is down she takes her alphabetized list of students randomly selects 50 students determines the number of classes each of the 50 selected students is taking and calculates E 54 She then reports to the PTA HSince I took a large random sample the population mean number of classes taken by the students at KHS is 54 Write a short paragraph to send to her that explains why her statement is not correct ANS The Principal39s statement is not accurate since the mean was calculated using data from a sample and not the entire population Statistics calculated from samples are subject to variability and are only occasionally equal to the true value After all different samples will produce different statistics depending on who is chosen for the sample REF Section 81 AP 614 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 23 Consider the following quotpopulationquot 2 2 4 5 Suppose that a random sample of size n 2 is to be selected without replacement from this population There are 6 possible samples since the order of selection does not matter Compute the sample mean for each of these samples and use that information to construct the sampling distribution of 3 Display it in table form ANS The 6 possible samples include 2 and 2 2 and 4 2 and 5 2 and 4 2 and 5 4 and 5 The distribution of X is REF Section 81 AP 24 Consider the following Hpopulation 1 1 3 4 Suppose that a random sample of size n 2 is to be selected without replacement from this population There are 6 possible samples since the order of selection does not matter Compute the sample mean for each of these samples and use that information to construct the sampling distribution of E Display it in table form ANS The 6 possible samples include 1 and 1 1 and 3 1 and 4 1 and 3 1 and 4 3 and 4 The distribution of i is REF Section 81 AP 25 Consider sampling from a skewed population As the sample size It increases some characteristics of the sampling distribution of change Does an increasing sample size cause changes in the characteristics of the sampling distribution shown below If so specifically how does the sampling distribution change a The mean of the sampling distribution of b The standard deViation of the sampling distribution of c The shape of the sampling distribution of ANS a As the sample size increases u stays the same b As the sample size increases D will decrease c As the sample size increases the distribution of becomes less skewed and more normal REF Section 82 AP 615 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 25 How are the duahttttesgt 3 and uigtrelated7 ANS 4 ep REF SecuonRZAP 27 Consider samplmg from a populatmh whose preponmn ofsuccasses 15 p o 1 As the sample stzegt ngt tmxeasesgt some charaaenstms othe samplmg dstnbuuon of 3 change Whmh of a The mean of the samplmg distnbuuon of 3 b The standard devxauon of the samplmg dtsmhutmh of 3 c The shape othe samplmg dtsmhutmh of 3 ANS a As Lhasamplesxze thereasesgt hi stays the same b Asthesamp1estzemeasesgt a gets smaller normal REF Sectmh 2 ZAP 22 theory localewolvenneu39adts mrandom locale mAlaska samplmg dxmxbuuon of 3 b What 15 the mean of the samplmg distnbuuon of 37 c What 15 the standard dewatmh onhe samplmg dtsmbutmh of 37 ANS a up UU45345321Uandn17p7 UU174537 472m REF Sectmh 2 ZAP 29 Consider sampling from apopulation whose proportion of successes isp 05 As the sample size It increases some characteristics of the sampling distribution of 3 change Which of the following characteristics will change as It increases and what is the nature of the change a The mean of the sampling distribution of b The standard deViation of the sampling distribution of c The shape of the sampling distribution of ANS a As the sample size increases y stays the same b As the sample size increases 1 gets smaller c As the sample size increases the sampling distribution of becomes more normal REF Section 82 AP 30 The principal at Thomas Jefferson High School has been asked to estimate the proportion of students at KHS who drive to school and use the school parking lot He takes a random sample of size n 32 students and calculates a sample proportion 08 Now he exclaims Hsince my sample size is greater than 30 the sampling distribution of the sample proportion is approximately normal Write a short paragraph that explains why his statement is not correct ANS The Principal39s statement is not accurate since he uses the wrong rule to check for normality To determine if the distribution of p is approximately normal he needs to check if P2 2 10 and 20 p 2 10 For example ifp 8 then 1p3213 154 d ID and the distribution ofp would not be approximately normal REF Section 82 AP 31 When the sample size is Hlarge enough the statistic p has an approximately normal sampling distribution How does one determine if a sample size is large enough ANS After a sample of size n is taken a sample proportionp is calculated The sample size will be large enough to believe that the sampling distribution is approximately normal if the products np 2 10 and nl 7p 2 10 Another way to say this is that the sample has produced at least 10 successes and at least 10 Hfailures REF Section 82 AP 617 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 2 Determine the mean and Standard deviation ofthe sampling dismbution of 3 when 100mdp065 ANS p01 REF Section 2 ZAP z The theory 1ocatewo1venne tracks inrandom1ocations mAlaska sampling distnbution of 3 1 What is the mean othe sampling distntnition of 137 c What is the standard deviation ofthe samp1ing distntnition of 137 asoosv ANS a up 1nn45345 32111 and 1111 1111107453 5472111 5113 45 4531 7 453 mm d P3lt 4113120551134 13 2 4113 45 45317 453 mu Fzlte1rzgt115271527 2174 REF Section 2 2 AP Suppose AA A A H asample to assess their bellef They are wnsldenng asampleslze ofn sampllng dlsdlbuuon of 3 colrem d Ithe realesme agean are correctwhatls39hepmbablllly that asampleproporllmgt 3 would dlffer from o 70 by as much as o 057 ANS a np 4EI7 2821Eandnlrp 4Dlr7 1221EI A P3lt ar3gt75P 13 DA 7le7 7le7 4U 4U Fzlte 59Fzgt 59 2451 2451 49m REF Semen 2 2 AP 25 as moluse Under ddls ddeorygt handedness would be genemally passed on fmm parems m chlldxen That lsgt le ehanded parean would be more 11181le have le ehanded chlldrm man MA A A Q m l we and mm A A V F l m m probablllty of a nghvhanded offspnng 15 p o 50 3 dlsmbutlon b l 15 the probablllly of obsewlng a sample propomon of at least 3 o 5527 619 ANS a up 55 821Dandn1ip7 l5i 821D 65875 b P32658P22 Pzzz7snn3n REF Semen 2 2 AP 25 h m 3 o a u mg An mm distribution b If the modern uue populalmn properan ofnewbomboys 15 p o 52gt what 15 the probability of observmg a sample propomon of at least 3 57 ANS 3 np505225210mdnlt1rp501 7 524210 13921 191sz REF Semen 2 2 AP Chapter no1 imam a v nulall u Prnnnr nn TRUEFALSE l Uslng an unblased slausuc guaranlees lhal lhere wlll be no syslemauclenclency lo under or oyeresumale lhe value onhe populauon characterlstlcand lhal esumales wlll almosl always be relauyely close lo lhe lrue value ANS F REF Secuon 9 1 AF lhal 15 close lo lhe aclualyalue othe populauon characlerlsuc ANS T REF Secuon 9 1 AF for smaller sample srzes ANS F REF Secuon 9 1 AF 4 The standard error of 5 ls ANS F REF Secuon 9 1 AF ANS T REF Secuon 9 2 AF 5 The large sample conmlence lnlerval formula for esumaung p can always safely be used u up 2 In ANS F REF Secuon 9 2 AF 7 Uslng ahlgherconmlence leyelwrllresull m analrower con dence lnlerval ANS F REF Secuon 9 2 AF 2 Holdlng all olher elemean equalgt an rncrease in sample srze wlll resull m a wrcler conmlence lnlerval ANS T REF Secuon 9 2 AF MULTIPLE CHOICE 9 Three dxfferent mums are bemg considered for asumaung a population dqaracterxsuc Smmur n mmm y 39a Hl uf 1 Value of M llararteris z pop tlmrmtm39i ir umm m Valuc 0 11011 lermlm39istin thch stamucwould you rewmmendv a susz b summon c summon d Stamuclor summon sumac u or sumac m ANS A REF Seame 1 AP 10 any y m y the actualvalue om andp as u Z andp HIKZEandpEI7 a I only b u only m on1y u and u on1y A111hree esumates W111 be equa11y c1ose1o 1he ac1ua1 value of REF Sec on 9 1 AF 11 An unbxasedstausuc 15 one that 15 c1ose1y approxrrna1ed by a nonna1 Ame has 1he smallest vanance 15 moundeshaped 15 near1y symmemc does not consulmlly laud 1o underesumate or to overesumate 1he value of a popu1a on oharactensuc macaw E REF Sec on 9 1 AF 12 To esumate 1he proporuon of racuuy a1 a stale unrversuy who own a homegt a random samp1e of racuuy 15 seleaed For whrch othe followmg cornhrna ons of n and 3 would 11 be appropnale to use 1he con dence m1erva1 51zsnuea1va1ue 1o asumale 1he popu1a on propomom e nZEIEIandg3EIB ANS E REF Sec on 9 2 AF 12 Jasmme has decrded 1o decrease 1he con dence 1eve1 1n her es ma on of a popu1a on propomon What 15 1he effect on 1he w1dLh of 1he assocxaled con dence mien317 a The w1dth of 1he con dence m1erva1 1ncreases b The w1dth of 1he con dence m1erva1 decreases c The w1dth of 1he con dence m1erva1 15 unchanged ere 15 no1 enough mformauon to say REF Sec on 9 2 AF 14 Chuck has decrded 1o rncrease 1he srze of 1he samp1e he uses 1o esumate a popu1a on propomon What 15 1he effea on 1he w1dLh of 1he assomaled con dence mien317 a The w1dth of 1he con dence m1erva1 1ncreases b The w1dth of 1he con dence rn1erva1 decreases c The w1dth of 1he con dence m1erva1 15 unchanged d There 15 not enough mformauon 1o say ANS E REF Sec on 9 2 AF 15 A 90 con dence interval for a population proportion calculated using data from a random sample of size n 51 is 0573 0787 Which of the following is the 95 confidence interval calculated from the same data 0602 0758 0620 0740 0553 0807 0543 0817 0486 0874 99965 ANS C REF Section 93 AP 16 Suppose that a random sample of 85 high school classrooms in the state of Iowa is selected and a 95 con dence interval for the proportion that has Internet access is 073 079 Which ofthe following is a correct interpretation of the 95 con dence level a The method used to construct the interval will produce an interval that includes the value of the population proportion about 95 of the time in repeated sampling b You can be 95 con dent that the sample proportion is between 073 and 079 c There is a 95 chance that the proportion of all high school classrooms in Iowa that have Internet access is between 073 and 079 d You can be 95 con dent that the proportion of all high school classrooms in Iowa that have Internet access is between 073 and 079 e None of the above is a correct interpretation ofthe confidence level ANS A REF Section 93 AP 17 What proportion of college students have used cell phones to cheat on an exam Suppose you have been asked to estimate this proportion for students enrolled at a large college Make an estimate of the margin of error M when there are 151 students in the survey Assume a 95 con dence level a M 008 b M 2 008 c M S 008 d There is not enough information to make an estimate of M ANS C REF Section 94 AP 18 A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor If a handle is cracked it is considered defective and can t be used A lar e shipment of plastic handles is received How many handles from the shipment should be inspected in order to estimate p the proportion of defective handles in the shipment with a margin of error of 013 or less Assume a con dence level of 95 a 4 handles b 113 handles c 57 handles d 228 handles e 100 handles ANS C REF Section 94 AP 624 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part SHORT ANSWER 19 What 15 the d1fferenoe between an unb1ased statrstrc and a brased 5131151107 ANS h a no m m w a w111 average to a va1ue that 15 drrrerent mm the populauon parameter REF Sectmn 9 1 AF 20 ANS accurate REF Sectmn 9 1 AF 21 use1fyou wanted to estrmate the populauon meam ANS 1m A e h t norma1gt may be a better ohmce REF Sectmn 9 1 AF 12 bmlogy A 1 Regulus mzpa They found that 72 ohm 152 landmg were 1n the m1d he1ght regrnm 2140 meter gound 5 above a 1n the 21 7 40 meter he1ght range b landmgs orthese1nng1ets that are 1n the 21 7 40 meter he1ghtrange ANS 78 a 9 E e n 4785 n 4U18 5552 n 4785 n 5215 b 95 c1 11 4785 1 9611 625 o 4012 and o 5552 REF SectlonQZAP 22 A recent study lnvestlgated the effects of a Buckle Up YourToddlers campalgl to get parents in a large cltygt and found 192 out or594 parents buokhng up Lhelr toddlers 3 9 who buckle up thelrtoddlers ANS a e n 3232 n 285ml 36nd n 3232 n 5758 b 95 cl I 323211 96m 524 between 0 225 and o 251 REF Sectlon 9 2 AP 24 m m a the blrdsgt the lghl othe blrd might alert predators to the presence of a nest To see u researcher was recorded Slxlyrfour othe nests hlled la the parent abandoned thenest populatlon b ln nonnal n answer Wth an approprlate statlstlcal argurnent ANs 3 Thls semng meets the condltlon that up 21D and nl 2 lngt so a 95 cl can be calwlated 196 U5336U7213 Tlnlsrneansthatlarn 95 07213 3 sample REF Sectlon 9 2 AP 15 Bne y de ne the followlng terms in your own words a Ccnfldence lnterval b The confldmce level assoclated wlth a confldmoe lnterval ANS 3 V result 15 a reasonable outcome glven procedures for each samplegt whlch lnclude the populatlon characterlstlc belng estlmated REF Sectlon 9 2 AP 25 the respondents Construct and lntelpret a 99 cl fothe true proportlon orvoters who prefer the Republlcan candldate b m R m argument ANS a Thlssemng meets the condltlon that up la and cl 7 2 1n so a 95 cl can be 2 pg lZEI lZEI I calwlated t z 58 e H 39mm 6344 Thls meansthat l am 95 N candldate cannot be completely conhdent omctory REF Sectlon 9 2 AP 27 A researcher would llke to determlne the preportlen ofcollege studenw who Orthe on ma nt populatlon proportlon ANS The pleeedute ls applopnate lr up In and n 17 2 In and lrthe sample ls alandem sample The sample ls a random sample and ex thls sample a f 378 e and l 7 So sun the assumptlons are met n 756 The con dence lnterval ls then u 756 l 96 REF Seetlon 9 2 AP 22 Eyestlaln ls thougql to be assoelated wlth dlffermt types ot ottlee work The Alme l w e entry employees that have eyesuam a They would llke to estlmate p to wlthln o 05 wlth 95 wnfldence lt they accept the o 21 as a reasonable lnltlal estlmate om what sample slzle should they use stanlng valu for thelr study7 b t l e t t r t ANS a a W p1p a l 95 z n zllrn Zl 154 92 Thusgt a sample ot at least 255 wlllbe needed 3 for n above would provide a suttlelent sample slzle REF Seetlon 9 4 AP 29 melesound The ldea lsthat arewrdlng otthe mother svoloe calllng the ohlld snamemay be an lmplovement over Existing systems a The researchers would llke to estlmate 2 lo wnnln o 05 wth 95 confldmoe Past expenence has shown that convenllonal alarms are errecuve about 0 52 ohm Mme lnnls 15 Study7 b l h H r V sampleslzel ANS a nplt1epgt 2 e u smell 538 374 2155 39l39nusgt a sample of 3118351375 ohllliren will be needed b for n above would provlde a sufflclml sample slze REF Secuon 9 4 AF 20A survlval proponan to Wldnln o5 Wl39h 95 confldmoe ANS 72 28 Solvelsd if REF Secuon 9 4 AF n n lo oblalnnZZOQKsoasamplesle orleormore 31 m m h h l R m l m m Wl39h 95 confldmce ANS 1585 Solve l 96 uzs lo omaln n 723 7 Asampleslze orm onnore should be used n REF Secuon 94 AF Chapter 10 Asking and Answering Questions About a Population Proportion TRUEFALSE N w 4gt U1 9 gt1 00 gt0 If the null hypothesis is not rejected there is strong statistical evidence that the null hypothesis is true ANS F REF Section 101 AP A type 11 error is made by failing to reject a false null hypothesis ANS T REF Section 102 AP The level of signi cance ofa test is the probability ofmaking a type 1 error given that the null hypothesis is true ANS T REF Section 102 AP For tests of hypotheses about u decreases as the sample size increases if the level of signi cance stays the same ANS T REF Section 102 AP is called the observed signi cance level ANS F REF Section 102 AP All other things being equal choosing a smaller value ofoc will increase the probability of making a type 11 error ANS T REF Section 102 AP Small P values indicate that the observed sample is inconsistent with the null hypothesis ANS T REF Section 104 AP It is customary to say that the result of a hypothesis test is statistically signi cant when the P value is smaller than a ANS T REF Section 104 AP The power ofa test is the probability of failing to reject the null hypothesis ANS F REF Section 106 AP 630 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part MULTIPLE CHOICE 10 You are interested in determining whether there is strong evidence in support of the claim that less than 40 of retired adults have a part time job To answer this question what null and alternative hypotheses should you test a H ip04 versus H lpr 04 b H ip04 versus Hd2plt 4 c Huip04 versus Halp 04 d Harp lt 04 versus Haip gt 04 e H ip lt 04 versus Hiip 04 ANS B REF Section 101 AP ll Which of the following specify legitimate pairs of null and alternative hypotheses a HDIp02 H pb l b H zpa DGS H pgt 35 c anp lt 040 H tp gt U40 d H p 050 H1p050 e Hozp04ll HazpgtEL S ANS A REF Section 101 AP 12 Describe the two types of errors that might be made when a hypothesis test is carried out a A Type I error is rejecting H0 when H is true A Type II error is failing to reject H0 when H is false b A Type I error is rejecting H0 when H is false A Type II error is failing to rejectHa when H is true c A Type I error is failing to rejectHa when H is true A Type II error is rejecting H0 when H is true d A Type I error is rejecting H0 when H is true A Type II error is failing to reject H0 when H is true e A Type I error is rejecting H0 when H is false A Type II error is failing to reject H0 when H is false ANS A REF Section 102 AP 13 Every year on Groundhog Day February 2 the famous groundhog Punxsutawney Phil tries to predict whether there will be 6 more weeks of winter Suppose that you plan to take a random sample of 23 years and use weather data to determine the proportion of these years the groundhog s prediction was correct If the groundhog has a 50 50 chance of making a correct prediction the spread of the sampling distribution of g3 for samples of size 23 is 631 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part a CIquot 01474 b Dquot 01043 c D 02085 d a 00435 e 13 00870 ANS B REF Section 103 AP 14 Assuming a random sample from a large population for which ofthe following null hypotheses and sample sizes is the large sample Z test appropriate a H p 005rz5 b Hozp 006 r 50 c H p002n25 d Huip 03320 e H0390 06 n 200 ANS E REF Section 105 AP 15 In a test ofHO p 045 versus H p lt 045 the value of the Z test statistic was calculated to be Z 055 Which ofthe following is the P value for this test 01230 02360 02500 02912 03020 99965 ANS D REF Section 105 AP 16 Assuming a random sample from a large population for which ofthe following null hypotheses and sample sizes is the large sample Z test appropriate a 1 Ulp 009f340 b Hozpn01n50 c Hozpo01m30 d H zp 04 y 100 e H p 081 340 ANS D REF Section 105 AP 17 Assuming the same sample size is used how does changing the significance level from 02 to 005 affect the power ofa test a The power decreases b The power increases c The power does not change d The power does change but it might either decrease or increase 632 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part e It is not possible to predict whether the power will increase decrease or remain the unchanged ANS A REF Section 106 AP 18 Assuming the same signi cance level is used how does increasing the sample size from 50 to 100 affect the power ofa test a The power decreases b The power increases c The power does not change d The power does change but it might either decrease or increase e It is not possible to predict whether the power will increase decrease or remain the unchanged ANS B REF Section 106 AP SHORT ANSWER 19 Explain in your own words what a hypothesis test is ANS In a hypothesis test we are using data from a sample to make a decision between two competing claims about a population characteristic REF Section 101 AP 20 Explain in your own words the distinction between a null and alternative hypothesis ANS The null hypothesis is the claim about apopulation characteristic that is initially assumed to be true The alternative is the competing claim about the population characteristic REF Section 101 AP 21 One of the early decisions that must be made when performing a hypothesis test is the choice of significance level Brie y describe the considerations that go into making this decision ANS To decide on the significance level the consequences onype land 11 errors should be considered lfa Type 1 error is worse a small signi cance level should be chosen at lt 05 and ifa Type 11 error is worse a large significance level should be chosen at gt 05 REF Section 102 AP 633 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 22 Children as young as 2 years of age upon seeing an object placed under a pillow in a familiar setting at home will understand to look for it after an interval of time and be able to nd it Investigators believe this capability will be less pronounced in a laboratory situation where the child is away from the familiar setting of home Let p denote the proportion of 2 year olds than have this understanding in the home situation and suppose that p 035 The investigators wish to determine whether the proportion that remembers is less when the child is away from home a What is the appropriate null hypothesis b What is the appropriate alternative hypothesis c In your own words distinguish between a Type land a Type II error in this context ANS a H0 p 035 b Haplt035 c A Type I error is to decide that children remember less when outside of the home environment when in fact they remember equally well A Type II error is to decide that children remember as well in the laboratory setting as in the home setting when in fact they remember less away from home REF Section 104 AP 23 De ne using your own words a test statistic ANS A test statistic is a measure of how much the sample differs from the null hypothesis REF Section 104 AP 24 In your own words what is aP value ANS A P value is the probability of observing a test statistic as or more extreme as the one observed in the sample assuming that the null hypothesis is true REF Section 104 AP 25 As children grow they develop what is known as Hrepresentational insight a connection between an object and a symbol for that object A random sample of youngsters 24 months old were shown avideo ofsomeone putting a toy under 1 of4 randomly placed boxes in a room familiar to the child They were then taken to the room and asked to H nd the toy The investigators reasoned that a child with representational insight should pick the correct box on the rst try If the children were to overturn the boxes randomly they would nd the toy on the rst turn 25 of the time Thirty children out of 57 subjects found the toy by turning over the correct box on the rst try 634 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part test llne appropnale hypothesls ANS 1 1 Hn pn07 5 3 Ha 12ngt025 4 a005 r n 25 5 n 25l e n 25 a Randomsample7 lem ln39hepmblanl Large sampleslzev Yes 7112 14 25 gt10 and MO em42 75 gt10 5257 25 7 25l e 25 57 2 FrvalueFzgt4 me 0 48 9 l l we re eel Hn n V Lhatlltrmonth old ohlldrm have representatlonal msxghl REF Semen 10 5 AP 25 One cntlclsm ofreadlng wmprehmslon less 15 that whlle uney may measure readlng comprehenslnm uney also measure nllner falters nolrelaled m reacllng comprehmslon A readmg and llne examlnees answeraselnrmuluplecnmce llems abounlnepassage Tosee lfpamcular hlgherrate unan chance 20gt slnce unere were 5 memes for each quesunn questlom Test llne relevanlhypolhesls uslng me o 05 ANS l pn me bue propomon of psychology studmts who answerme quesllon correctly 2 Ha pn 0 20 3 Ha 12o gt 0 20 4 a005 p n 5 ZEI1 20 n a Randomsample7 lem mmeproblem Large sample slzev Yes 7112 20 gt10 and 710 pquot 20 gt10 37 2 7 21 2 lEIEI 2 Emma Fzgt 2 50 0052 250 9 u l werejeclHn n l c m REF Secuonl05AP 27 a hh you would check me assumpuons ANS There are 2 commons wmclr need to be met l The data needs to be from a random sample from me populauon of lnterest 2 Thesampleslze needs to be large To checlumssee lfnpn gt l0 and 710 epngt l0 REF Secuon 105 AP Chapter 11 Asking and Answering Questions About the Difference Between Two Pnnlllatinn Prnnnninn TRUEFALSE Two samples are sald to be lndependent when the selectlon of the individuals ln one sample has no beanng on the selectlon ofthose ln the other sample ANS T REF Sectlon ll 1 AF 3 732 ls a hlased estlmator otp 7 ANS F REF Sectlon ll 1 AF When constructlng a con dence lntelval for the dlffelence oftwo population plopoltlons the appreprlate standard error of 3 732 ls ANSl T REF Sectlon ll 1 AF The hypothesls p pz ls equlvalentto the hypothesls p p2 u ANS T REF Sectlon l l 2 AF The Frvalue for a hypothesls test concemlng the dltterence ln two populatlon proportlons ls always calculated by tlndlng the area to the r 1t ofthe test statlstlc regardless ofthe altematlve hypothesls ANS F REF Sectlon l l zAF the standard deviation used ln the large sample wnfldmoe lntel39val for p e p ANS F REF Sectlon ll 2 AF MULTIPLE CHOICE 7 For whlch of the followlng sample slzes and 3 values would lt be appropnate to use b 5043 232073 c 73 1 z enuealvalue to estlmate a lererence m populauon proponmn57 U 3n 932 lz 2 my n95 c In only d u and In only e Igt ugt and m ANs E REF Sectlon ll 1 AF 2 A 90 con dence mterval for p ep2 15 43 05gt 4 om Whloh othe followlng 15 the 95 con dence mterval calculated from the same datav a 4 052gt o 005 ANS E REF Sectlon ll 1 AF 9 A laymg m Juvemle Rhode Island Red h l t l weeks of v layer pelletsgt 4 hens were laymg at 13 weeks of age The 95 con dence mterval for the lererence m laymg propomons at 13 weeks 15 ens 1n a group of 24 hens that were fed scratch galngt 12 a Ellaan ItEIlK a In ANS E REF Secuonll lAF 10 A study determlned that m 2009gt 22 of those m a random sample of 100 adult of slze 100 The 95 con dence mterval for the dlrterence m populauon proportlons Paola Pamol is U15i 8 0290136 U15iU136 029088 0000136 9999 s ANS C REF Sectionlll AP 11 To learn about the proportion of college students who are registered to vote surveys were conducted in 2010 and in 2011 Suppose that in 2010 39 of the people in a representative sample of 450 college students were registered to vote In 2011 33 of the people in a representative sample of 235 college students were registered to vote For the 99 con dence level determine the margin of error of the difference of the proportions a 00751 b 00495 c 00989 d 04131 e 00383 ANS C REF Section 111 AP 12 A study was carried out to see if seniors were more likely than freshmen to favor banning cell phones at school Which of the following hypotheses should be tested to answer this question a H02pS pFOversusHApS ppgt b HDIpS pFDwersus HaipspF 20 c HD S FUversusH js zEl d 11103555ltElversusHa1 S pa e Hops ppUversusH pS pp El ANS A REF Section 112 AP 13 A study is conducted to determine whether the proportion of airline passengers complaining with post ight respiratory symptoms is larger for ights that do not circulate cabin air than for ights that do circulate the air After checking to make sure that all of the necessary conditions were met we calculated the value of the 2 test statistic to be Z 084 Which of the following is the P value associated with this test a 0 b 02005 c 0401 d 07995 e 0599 ANS B REF Section 112 AP 639 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 14 Each person in a random sample of 200 students and a random sample of 150 faculty at a large university was asked Do you take public transportation to campus Fifty eight percent of the students and 46 of the faculty responded Yes This data was used to carry out a test of the hypotheses H0 12le2m pm 0 versus Hapm pmm at U The value of the test statistic was Z 2226 For a signi cance level of 001 which of the following is correct a H0 should be rejected there is convincing evidence that the proportion of people who take public transportation to campus is different for students and faculty b Ho should be rejected there is convincing evidence that the proportion of people who take public transportation to campus is the same for students and faculty c Ho should not be rejected there is not convincing evidence that the proportion of people who take public transportation to campus is different for students and faculty d H0 should not be rejected there is not convincing evidence that the proportion of people who take public transportation to campus is the same for students and faculty e There is not enough information provided to be able to decide whether Ho should be rejected or not ANS C REF Section 112 AP 15 A hotel chain is interested in evaluating reservation processes Guests can reserve a room by using either a telephone system T or an online system 0 that is accessed through the hotel s web site lndependent random samples of 90 guests who reserved a room by phone and 68 guests who reserved a room online were selected Of those who reserved by phone 61 reported that they were satisfied with the reservation process Of those who reserved online 44 reported that they were satisfied Based on these data is it reasonable to conclude that the proportion who are satis ed is greater for those who reserve a room online Which of the following hypotheses should be tested to answer this question a H ipT poDversusH01pT poa b Husz poUversusH01pr pob c H sz pogtDversusHUp p0s l d H pTp0 versusHopr poU e HDIpT po ltUversus Hop 3000 ANS D REF Section 112 AP 16 A study seeks to determine whether the proportion of Dutch boys who listen to music at high volume is greater than this proportion for Dutch girls After checking to make sure that all of the necessary conditions were met we calculated the value of the Z test statistic to be Z 2999 Which of the following is the P value associated with this test a 0 b 00014 c 00028 d 09986 e 09972 ANS B REF Section 112 AP 640 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part SHORT ANSWER l7 md mdmt samples and parred samples What makes two samples lndependenm ANS m m w a a l parmular rndmdual m the sewnd sample REF Sectlonll 1A 18 l a sklp7 The total sample slzes and the numbers who responded Less than l week ago are glven in table below Number rupnnding quotLass man 1 wukquot these samples as representatlve othe wrrespondlng populauons b Does mere appear to be a dlrrerence betweenlhe propomons ofmen and women respondlng LessLhan l weelw Provldestatlalcaljustl catlon for your answer m j 2 In mi 2 1D and 1732 2 ln ans rspresenlnerewrllwalnesngt nle 240 54 and 189 The 95 wnfldence lnterval 15 glven by 2 17 2 2 17 2 3 732 zcnmvalue M ow quotl quot2 l7275l 7 17275 25295l 7 25295 l7275e 25295 l 95m T T 70 021730950le 022m 701451fO 0154 mlerval Th151nd1mtes that Lh15 va1ue othe d1fference 15 not wnsment mm the data that has been observed REF Semen 11 1A 19 1n many annna1soc1euesgt a role assumed bythe adult male 15 a smuywam1ng adu11 11111115 111 a Fund Scunnng quotLeaking both myxquot Bzhavinr ANS propomons 1 Let p propomon offemales who scan when a1onegt p2 propomon offemales who scan whm w1Lh a male 1 Ha 171132 31 H 171 gt 132 41 S1g1manoe1eve1u o 05 Test 513115110 2 n321un1s3j21nn32 2 1n and 1732 2 1n T1115 wpresmlhere w1Lh values 5112037gt and 29 2 FevaluegtFzgt3 RRR 0 0004 9 Smoe Lh15 Mame 151855 than 11 0 05gt elem me null hypothesns There 15 ev1dmce 11m renns1es scan more when alone 111 when acwmpamedby a male REF Semen 11 1A 20 w 4 n p n 1 n m metablebelow Number mpnnasng quotLass an 1 wukquot 1 nnn 1 week 1 mese ssmp1es as representauve of39he wrrespondmg populauons b Does mere appear to be a d1ffe139ence betweenthe propomons ofmen and women respendmg Less39han 1 weew medestatmmaljusu cauon for yeumnswer 3 1n 2111 T1115 15 presmthereW1lhvaluas104gt n 173j2111gtu32 21Ugtand 1732 307gt71gtand182 The 95 wn dence mterval 15 gwen by 2 17 2 2 17 2 3 232 zcnmvalue M M W1 W2 2531140 e 253114 280530 e 2815 2531147 281153 1 9511 T T e0 027520 9500 025455 e0 0971gt 0 0419 b Negt mere doesnwseenn to be a 311mm d1fference 1n me genders 1n terms ofwhal 643 t l observed REF Section ll iAP 21 Al allll caps Ofthe 500 students 378 saythey support cappingtextbookpnces and ofthe 500 racultymembers 256 say they support capplngprlces a Determlne ifthe large sample con dence interval procedure can be med for estimation b c interpret the con dence lnterval s a There are at least 10 successes and failures ln each goup so the large sample con dence lnterval procedure can be med for estlmatlon b The 95 con dence lnterval ls then 7s tir 7s slzlruslz sun sun U7564512le 7U186 ll zj c l andozoz REF Section ll iAP 77 ofmen who llst Action as thelr favorite mone genre and the proportlon ofwomen who ll t tl n an 200 women Ofthe men 156 lndlcate that Action ls thelr ravonte genre ofthe women 87 lndlcate that Action ls thelr Wants a Determlne lrthe large sample con dence interval procedures can be med for estimation b c interpret the con dence lnterval d are equal NS a There are at least 10 successes and failures ln each goup so the large sample con dence lnterval procedure can be med rol esuma on b The 95 con dence Interval ls then u sznl e n szn mu nsznrn4351196 W in Inw 174 c 0 174 d Became his con dence lnterval contams 0111etw0 plopomons maybe equal REF Sec on ll 1A 2 ln many anlmal socle esgt a role assumed bythe adult male 15 a semygt wamlng adull wmung naun l Hug m a than when accompamed by an adult female Data from th5 study ls glven below Male Scanning quotLeakingan myxquot Behavior ANS propomons l wth a male N Hu 171 Ha plqzz Slgnflcanoe level u o 05 pzlugtnl p 2mwizzlmandnz epzjzluThrsrspresentherewlth values 55gt28gt51gtand 15 5557 me 1 937 7 73lzsl 73125 73125 73125 84 7o 2 FevaluegtFzlt7193700264 males scan more when accompanled by a male than when alone REF Seaman ll ZAP 7 A l 1 ll l support and 500 facultymembexs and aslrs whether or not they support textbook prlee caps or the 00 mm m members 256 say the ysupport capplng pnces a What are the hypotheses the researcher should me b Are the assumptlons met for a large sample test7 0 What is the Pevalue for the hypothesls test7 d What conclmlon can be drawm a Ho Pstmkm was Versm Ha pmn Wham b Yes the assumptlons are met for a large sample test there is arandom sample 0 The test statlstlc for thls test ls z and the Pevalue is less than 0 001 d We eanleleet the hullhypothesls There ls eVldehee that the plopoltloh of caps REF Seaman ll ZAP men and women who lhdleate Action as thell ravollte mone genre exists The stlateglst gathels a landom sample of 300 men and 200 women orthe men 156 lndleate that Action lsthelt ravollte genre orthe Women 87 lhdleate that Action lsthelt Vents a What ate the hypotheses the leseatehel should me b Ale the assumptlohs rol a large sample testv c What ls the Pevalue rol the hypothesls test7 d What conclmlon can be dxawm ANS a Ho pm Wm Velsm Ha pm Pm b Yes the assumptlohs ate met rol a large sample test thele ls alandom sample 0 The teststatlstlc fol thls test ls z and the Pevalue ls 0 0625 th 0 05 Sigu cance level we would all to leleet the hullhypothesls We ate not conVlnced that the plopoltlohs ate Sigu cantly dlrreleht REF Seetloh ll ZAP t a speech delay olhot The data by gender ls glvm m the table below Spuch dday and gumquot at 3 yur old At the 05 slgnlflcance level do the data provlde evldmce of the nypolneslzed developmental dlrrerencesv Provlde statlstlcal evldmce for your conclusan propomons have a speech delay 2 Human 3 Ha plgtpa 4 Slgnflcanoe level a o 05 13 k2 Testslatlstlc z p411 p411 n n2 WK 2 lngt nl 73 2 lngt n25 2 lngt and 1732 2 ID Tnls lsleresenlneregt wth values 11220gt 72gt and 259 n7zaezzl4 7551 7 156507 1565 156507 1565 KHZ 337 2 Emma m gt75 51 l 0000 9 Since th5 Emma 15 more man a o 05gt do not led me null hypolnesls There 15 no evldence Lhalmales have a nlgner rate ofspeech delays man do females mesmdy pamnpanlsl REE Secuon ll ZAP h V age zgt each chlld was classlfled as havlng a speech delay ornol These dslsgt tosseclassl ed by a famlly hlslm39y ofspeech oommuhlcsuoh dlsordergt 15 glyeh h lhe table elow Spuch dday and gumquot at 3 year old No Total e 05 slgnmshoe levelgt do he dalapmvlde evldmoe onhehypolheslzed oh a y39JQlopmmlsl dlrrerehcesv Provlde statlsllcal evldmoe foryour wnclusl b ANS propomons l Let p 7 proponan ommlly hlstory populsuoh who have a speech delsygt pp 7 propomon orho famlly hlstory populsuoh who have a speech delay 2 Ha In Wk 3 Hz 129122 4 slgnmshoe level a o 05 Teststatlsuc z L p411 p411 n n2 2 la n25 21Ugtand 1732 2 ln Thls lspxesehlhere 404 quotl5 2 ml M1718 ywhvaluesza125mgt Zl S lK B 2272 z 7 lsdsl e lsds lsdsl e lsds 171 468 649 8 P value PZ gt 2272 00115 9 Since this P value is less than 0c 005 reject the null hypothesis There is evidence that children who have a family history of speech delay have a higher rate of speech delays than do those without this family history b This is an observational study The explanatory variable Hfamily history of speech disorder is not randomly assigned to the study participants REF Section 112 AP 28 Would it be appropriate to use large sample hypothesis testing procedures for the following dataset Why or why not A random sample of45 people was asked to indicate ifthey would return a lost wallet Of the 45 sampled 39 indicated that they would return the wallet ANS No this is not appropriate since there are not more than 10 failures in the sample REF Section 113 AP 650 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part Chapterlz A kin and 39 39 Ah 0 vnulan Mes TRUEFALSE 1 The d15mbut1on of 2 W111 a1ways have me same shape as me d15mbul1on of39he populauon bemg samp1ec1 ANS F REF Semen 12 1 AF 2 i cusmbuuen ANS T REF Semen 12 1 AF 2 As H gows larger The mean othe samplmg msmmuen of 2 gets closer to 11 ANS F REF Semen 12 1 AF 4 Theaandard devmuon othe msmmuen of 2 demeasas as n meases ANS T REF Semen 12 1 AF 5 The msmmuen of 2 15 normal 1the populauon 15 normal ANS T REF Semen 12 1 AF 5 L1m1t Theorem ANS T REF Semen 12 2 AF 7 largen ANS T REF Semen 12 2 AF 2 The tcm dmoe m1erva1 formula for esumaung Ta should only be used whemhe populauon bemg samp1ec1 15 at least approxmalely normally dmnbuted ANS F REF Semen 12 2 AF 9 A tourve 15 bellrshaped 111e me 2 Ame 1m 15 1ess spread out ANS F REF Semen 12 2 AF 10 The standard error of Tr is s ANS F REF Section 122 AP MULTIPLE CHOICE ll For a random sample from a skewed population for which of the following sample sizes would the sampling distribution of f be closest to normal in shape a n ll b n 18 c n 19 d n 22 e n 40 ANS E REF Section 121 AP 12 What is the standard deviation of E for random samples of size 80 from a population with a mean of 48 and a standard deviation of l 1 0138 123 0371 11 66 99965 ANS B REF Section 121 AP 13 The spread of the sample mean decreases when the population mean increases the population standard deviation increases the sample mean decreases the sample size decreases the sample size is increases ANS E REF Section 121 AP 994165 14 Commute distances for employees of a large company have a distribution that is quite skewed Suppose the mean commute distance is 20 miles and that the standard deviation is 7 miles What can be said about the mean commute distance for a random sample of size 49 employees from this plant a The distribution of X will be approximately normal with mean 20 and standard deviation b The distribution of X will be approximately normal with mean 20 and standard deviation c The mean and standard deviation of X will be 20 and 7 but the sampling distribution of 3 will not be approximately normal 652 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 2 wrllnot be approxrmatelynormal e 2 wrllhave astandard normaldlstrlbutlon ANS E REF Sectlon 12 1 AF l5 Let he represent themean value othe 2 sampllng dlstrlbutlon and la represent the populatlon mean What can be doneto reduce the lererence between he and m a lncreasethesample slze b decreasednesampleslze c decreasethe populatlon standard devlatlon d lncrease the populatlon standard devlatlon e nothlngslnce up u for any populatlon dlstrlbutlon ANS E REF Sectlon l2 l AF 15 A recent survey sampled LURE parents of schoolraged chlldren One questlon on the survey m h ur p c lldxen s school dunng the prevlous school year The followlng summary statlstlcs for trme volunteered permonth were glven Whlch of the followlng represents the 92 confldmoe rntervalv a 5 4455 755 e 915007 ANS D REF SectlonlzzAF 1 gt but e value of a 15 unlmown Yoursample slze 15 n 15 Whlch formula below should be used to nndthe 95 wnfldenoe lnterval for the meam 2le 15 b 2165 15 2256 15 d m l a ANS D REF Sectlon 12 2 AF 18 A packaging machine is supposed to ll boxes of breakfast cereal to a weight of 16 ounces Eight lled boxes are selected at random and the weight of cereal is determined The results in ounces are summarized in the following table 167 160 164 159 165 162 159 162 A technician wishes to test the claim that the machine is over lling the boxes At the 5 signi cance level what is the P Value of the test statistic Assume the lling weights are normally distributed 0262 0005 0032 0081 0115 99965 ANS C REF Section 123 AP 19 A report states that the mean yearly salary offer for students graduating with accounting degrees in 2012 was 49007 Suppose that a random sample of 60 accounting graduates at a large university who receivedjob offers resulted in a mean offer of 49800 and a standard deViation of 3100 What hypotheses should be used to test whether the accounting graduates at this school are securing starting salaries greater than 49007 a H0u49007 versus H i gt49007 b H i 49007 versus H11 lt49007 c H0ii49007 versus H ise49007 d Hou49007 versus H149800 e H04 49007 versus H iise49007 ANS A REF Section 123 AP SHORT ANSWER 20 Consider sampling from a skewed population As the sample size It increases some characteristics of the sampling distribution of 3 change Does an increasing sample size cause changes in the characteristics of the sampling distribution shown below If so speci cally how does the sampling distribution change a The mean of the sampling distribution of E b The standard deViation of the sampling distribution of E c The shape of the sampling distribution of E ANS a As the sample size increases u stays the same 654 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part b Aa1heaamp1earze hereasea a W111 decrease c m A 1 111 REF SeamanIZlAP 21 How areLhe quahuuesgt 1a and hegtre1a1ed7 REF Semen 12 1 AP m 1 a 11 he c1a1rh by Hardcore 15 Lruegtwhat15 he mean of he samphhg dmnbuuon of 2 for samp1es ofs1ze n 157 b of i forsamp1es 515122 n 157 c amen 15w111be1ess1hah597 a PGlt69PZltSJ pltzlte1mn91z A15 REF Semen 12 1 AP 22 11 r 1 M var1a1a1111ygt and shape Cohamer random samp1es creme 15 mm 1he pepu1aueh of freshmen 655 m h l and the sampllng dlsmbullon of 2 for a sample orslze n 15 sample mean geater than 20 hour5 7 The study of wilege e men also asked aboutthe sluden39as tlme spent playmg Video gamesgt and a relatlve frequmcy hlstogam onhe results appears below The mean amount ortlme spent playlng Video games was 0 2 hours per week Time vpent nu VillEn gnmes llrourssweelrt and spread othe sampllng dlstnbutlon of 2 5 To get full credltgt students should lndlcale that the mean wlll rem h 24 the sh am the same ape wlll remaln normal whlle the standard devlallon wlll demease a to a zgt maklng thegaph of 2 slnnnler andtaller b p2gtzupzgt 38 Pzgt313 lt ll not be approxlmately nolmal because the sample slze ls small n 4 The mean onhe e n u e l of the dlstrlblltlongt howevergt wlllbe halrorwhat lt was ln the onglnal populatlon a a slnce thls ls not a large sample n 4 and the populatlon ls notnolmally dlstrlbllted the r l t a t Hh l a rlglt but not as much as the populatlon REF Sectlon 12 1 AP 24 The prlnclpal at John F Kennedy ngl School has been asked to provlde the average h t l h Slncel ls 5 4 H erte a short paragaph to send to her that explalns why her statement ls not pollea ANS a ll slallsllcs dependlng on who ls chasm for the sample REF Sectlon l2 l AP 15 t m tlres sold on new cars ls 23000 mllesgt wlth a standard deviation orzs00 mlles a If the clalm by Get anp ls truegt what ls the mean othe sampllng dlstnblltlon of x for samples ofslze n 47 b If the clalm by Geeranp ls truegt what ls the standard deviation of the sampllng dlstrlblltlon of 2 for samples ofslze n 47 0 of a random sample ofslze n 4 ortlre llretlmes wlllbe less than 20000 mlles7 lZSEImlles c PGltZUUUUPZlt Pzlt72482 J REF Semen l2 l AP 25 perfectly polremgt but should clearly lndlcale dlfferenl aspeds othe curvesgt such as leaaueh vanahlhlygt and shape A MN m slze m l h l and lhe samplmg cllsmlmueh of i for a sample erslze n 15 w v y y lv v v r m 7 51 result m a sample mean gealerthan 20 m7 0 a l m r h from lhe megt and lhus dnvlng lhe pepulalleh down The gaph below 15 a relalwe dunng a masslve sh tagglng survey The mean length renhese sh was 0 2 feet N a 3 Length m Heme hem loot thlmhnhthh t 7 5 To get full credltgt students should lndlcate that the mean wlll remam the same X 7 he 4 gt the shapewlll remam hotmalgt whlle e th standard dewatloh wlll demease mg the gaph of 2 Skmnlet and taller KUrZA a 41 lt not be approxlmately normal because the sample slze 15 small h 4 The mean ofthe hna of the dlsmlmtlohgt however Wlllhe halfofwhat lt was m the ongmal populatloh PGgt3EDP2gt Pzgt 3 ml ll REF Sectloh 12 1 AP 27 Howarethequahtltles r and dwelatedv REF Sectloh 12 1 AP 28 When performing tests of hypotheses there are assumptions that must be met in order for the test to be appropriate For the test of a hypothesis about a population mean and given the raw data describe how you would check the assumptions ANS There are 2 conditions that need to be met 1 The data must be from a random sample from the population of interest 2 The sample size must be large at least 30 OR the population must be approximately normal To check for population normality the sample should be graphed to see ifit is plausible that it came from a normally distributed population REF Section 122 AP 29 Under what conditions is it reasonable to use the z con dence interval to estimate a population mean ANS It is reasonable to use the Z con dence interval to estimate apopulation mean when l the data are from a random sample of the population 2 either the sample size is greater than or equal to 30 or it is reasonable to believe that the population distribution is normal and 3 the population standard deviation 6 is known REF Section 122 AP 30 Under what conditions is it reasonable to use the con dence interval to estimate a population mean ANS The 1 distribution will be an adequate approximation of the sampling distribution of the sample mean when l the data are from a random sample of the population and 2 either the sample size is greater than or equal to 30 or it is reasonable to believe that the population distribution is normal REF Section 122 AP 31 A new species ofsea crab has been discovered and an experiment conducted to determine whether or not the animal can regulate its temperature That the animal can maintain a body temperature different from the surroundings would be considered evidence of this regulating capability Ten of these sea crabs were exposed to ambient temperatures of 24 degrees Celsius Their body temperatures were measured with the results below 2433 2461 2467 2464 2442 2497 2523 2473 2490 2444 For purposes of this example assume that it is reasonable to regard these 10 crabs as a random sample from the population of all crabs of this species a Calculate an estimate of the population mean 660 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessib1e website in whole or in part b Canstruet and rnterpret a 99 con dmoe 1nterva1rer u Prevrde statrstrea1 Jusu cauon foryour response 5 a 2 e 24 594 b 2769 99 c1 24 694 3 25 24 41 24 98 1am 99 con dent tnattne true rnean 4 1n temperature othe 13515 between 24 41 and 24 92 m ev1dmoe that the nabs rnustbe regulaung Lhe1r temperatures to some other value REF Semen 12 2 AP 22 One mdrcater of39he nea1tn of eld mme 15 the 1engtn unnerrtaus The followmg data Measures are 1n mm pepu1atren mean 1 Usmg tne gapnrea1c11sp1ay frompan agt would you adv1se tnat constructmg a 95 wn dence 1nterva11s appropr1ate7 Prevrde statrstrea1 Jusu cauon foryour answer ANS a One othe followmg gaphmal c11sp1ays would detennrne 1th15 15 plaus1bly a nerrna1 d15mbut1on Hrstegarn Normal Probabruty P1et Bexp1et 7 7 3225 4mm 1 n 1 mm scares b N d15mbut1on adequate1y desmbmg tne samplmg d15mbut1on othe sarnp1e rneans REF Semen 12 2 AP 661 A m dp l l tn lrth estrmate u to wrthln o 2 gams wth 95 con dence ANS a a 196EI15 n2 Zl lchousen217orlarger REF Sectlon l2 2 AP 24 populatlon 4gt 2 l2gt 5 7gt zgt 9gt 2 llgt 2 a Calculate an estlmate of the populatlon mean of radon gas levels b Construct and rntelpret a 99 confldmoe mterval for u p m a t appearthat the mean radon level for clty houses 15 under 5 ppm397 Provlde statlstlcal Jusllflcallon for your response ANS a 2 e 7 7ppm 2 9832 b 99 cl 77 3 25 e 4 534 In 755 ppm lam 99 certam that the true average A In radon value 15 between 4 524 and 10 755 ppm m f a mterval mcludes a range of values that are under 5 the data 15 conslstent vvlth some acceptable values ofradon level as well as some unacceptable levels REF Sectlon l2 2 AP 2 At Abraham Llncoln High School a popular achlevement test 15 used for college placement Counselors selected a random sample of 100 students from Abraham Llncoln Hrgn p m samplegt x e 525 and s 25v Construct a 99 con dence mterval for ugt the populatlon mean score for Abraham Llncoln Hrgn ANS n t A lnlerval can safely be constructed 2 szstzdzjls elsmtszl REF Sectlon l2 2 AP 25 The composltlon of the eanh s atmosphere may have changed overtlme One attempt to A t h glve the followlng percentages ormtrogen 524gt 550gt 5Mgt 522gt 542gt 525 502gt 59lgt 510 from the Cretaceous atmosphere a the Cretaceous atmosphere b The mean percentage ofnlu39ogm m the atmosphere today 15 about 79 Based on the mtrogen has changed from the late Cretaceous era 7 Explaln ANS own below Wlth x e D l4 s 5 44gt th5 makes the lnterval Normal probablllty plot sh l 31 i level ofnlu39ogm ln the Cretaceous atmosphere is between 55 95 and 55 22 Nltrggeg 4 2 J n l Nurmal Scares b The mean percentage ofnlu39ogm apparently has changedgt smce the modem valuegt 79gt 15 not in the con dence lnterval REF Sectlon l2 2 AP 27 Undelwhat condltlons ls the z contldence lntelval an applopllate way to estlmate a populatlon meam ANS lather than bemg estlmated from the sample REF Sectlon l2 2 AP 32 To 1 a seleaed from school dlstllct class llsts and glven a leadlng comprehenslon test The dlstllblltlon of Comma a 99 wnfldenoe lnterval for llgt the populatlon mean 18112792 1587119122 REF Sectlon l2 2 AP 1 111 t 29 M t l mllltary allspace Thlslalses lsslles of 5 whethelmldllte andgt for examplegt loud Jet nolses ale mn tlhl Lhe 559gt 511gt 575gt 555gt 524gt 549 521gt 552gt 522 loud J et nolses 1 The mean heart late for desert mule deer ls about 51 2beats per mlnllte Based on the on the heart late of desert mule dee Explaln ANS lntelval Nolmal plobablllty plot shown below Wlth 2 511 555 s 5 775gtlh15 makes the 95 contldence lntelval 511 555 2 31st6 55 11554 995 1am 95 contldent 1 n 1 Nutma1 Same b expectedgt smce the value 51 2 15 not 1n the calwlaled 1ntewa1 PTS 1 REF Semen IZZAP MSC Semen 122 40 a What 15 the apprepnate null hypotheam 1 What 15 the appmpnate a1te1nat1ve hypethesm 0 1n your own wordsgt d15t1ngu1sh between a Type 1 and a Type 11 error 1n Lh1s wnlexl ANS a Ha 1156 b 14L 11lt55 0 Type 1 Dec1d1ng that the area 15 subjectedto 201d ram when 1n fad the regmn 15 not subjeded to 201d ram Type 11 Dec1d1ng that the area 15 not subjected to 201d ram when 1n ractthe regmn 15 subjeded to 201d ram REF Semen 12 2 AP 41 p1 an n 1 m 1 pm t1me d1ffers from the t1me needed to class1fy songbn ds dds a What is the appropriate null hypothesis b What is the appropriate alternative hypothesis c In your own words distinguish between a Type land a Type II error in this context ANS a H0 u 750 b Hau 750 c A Type I error is to decide that the average classiflcation time for chickens is different than that of robins when in fact it is the same A Type II error is to decide that the average classi cation time for chickens is the same as the average classi cation time for robins when in fact it is actually different REF Section 123 AP 42 In cities and towns on the borders between states there is a significant amount of flight across state lines to avoid high state taxes on gasoline Some states such as lowa have large rivers for borders and tolls to cross the bridges Do these tolls impede traffic to other states to get cheaper gasoline To test this hypothesis an experimental Toll Free Week will be instituted at the Farmington Bridge where currently 50 cars per day drive out of the state Let u denote the true average number of border crossings per day at F arnlington if there were no toll a What is the appropriate null hypothesis b What is the appropriate alternative hypothesis c In your own words distinguish between a Type land a Type l1 error in this context ANS a H0u50 b Haugt50 c A Type I error is to decide that the average number of crossings would be greater than 50 if there were no toll when in fact the average number is still 50 A Type II error is to decide that the average number of crossings would stay the same 50 if there were no toll when in fact the average number of crossings would increase REF Section 123 AP 666 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part 42 from a local lake resulted ln the data 115ml below 25gt 55gt 42gt 54gt 5lgt 45gt 59gt 49gt 7gt 12 exceeds 5 ppb 7 ANS 1 ll true mean pas concmu39auon 2 Ha b 5 2 4 5 a sample7 Gwen ln me problem Random Normal populatlom Based on me samplegt ths seems reasonable 741 df9 2 Prvalue Ftgt e 41 o 5554 9 Slnce dne Prvalue gt a we fallto elem Hn We cannot conclude that the true mean w l 667 me sh should not be eatm REF Secuon 12 2 AP 44 A boalmanufacturer clalms that a pamwlar boat and motor comblnauon will burn resulted m me data below 4 05gt 429gt 425gt 454gt 423 z 93gt z 54gt 413gt z 92gt z 25 05 and lest the appropnale hypothesls ANS l lllmemeangallons offuelperhour 1 Ha V4 2 a ult4 4 0405 274 5 J a Randomsample7 lem mmeproblem Normal populauom Based on the samplegt th5 seems reasonable l l l l l W 35 375 4 425 45 475 4W7 4 7 wll c1er A In 8 P valuePt lt1lO8501 9 Since the P value gt X we fail to reject H0 We cannot conclude that the true mean consumption is less than 4 gallons of fuel per hour That is the sample does not give sufficient evidence that the manufacturer is correct REF Section 123 AP 45 Suppose that a study has been published linking arsenic which is commonly found in tap water to increased cancer rates The study also stated that arsenic levels below 10 ppm could be considered harmless Suppose that residents of Hacienda Heights CA are worried about the arsenic level in the local tap water a What hypothesis should they test b Describe a Type land Type II error in this context ANS a H0ulO HaugtlO b A Type I error is to decide that the mean arsenic level is above 10 and would result in purchasing the extra filtration system when in fact the mean is not above 10 and the filtration system is not needed A Type II error is to decide that the mean arsenic level is not above 10 and would result in not purchasing the extra filtration system when in fact the mean is above 10 and the filtration system is really needed Note This answer assumes that the water is considered safe until proven otherwise Students may reverse this and assume the water is dangerous until proven safe ie Ha u lt 10 To get credit the descriptions of the errors must match the hypotheses REF Section 123 AP 46 In your own words distinguish between quotstatisticalquot and quotpracticalquot signiflcance ANS lf observing a difference between a sample and a null hypothesis is unlikely to happen by chance alone the results are called statistically significant if the difference is enough to justify a different decision than would be the case were the hypothesis true the results are called practically signi cant REF Section 123 AP 669 2014 Cengage Learning All Rights Reserved May not be scanned copied or duplicated or postedto a publicly accessible website in whole or in part