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# Introduction to Statistics I STA 2122

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This 9 page Class Notes was uploaded by Jonatan Kunde on Monday October 12, 2015. The Class Notes belongs to STA 2122 at Florida International University taught by Dongmei An in Fall. Since its upload, it has received 19 views. For similar materials see /class/221815/sta-2122-florida-international-university in Statistics at Florida International University.

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Date Created: 10/12/15

STA 2122 1 REVIEW 11 not all inclusive TrueFalse The standard deviation of the sample mean is always equal to the standard deviation of the population The number of defective vending machines on a college campus is an example of a continuous random variable Every normal distribution has a mean 0 and standard deviation l A binomial random variable is a discrete random variable N E 4 V39 O Which of the following is a valid probability distribution a X lpX b X lpX 0 X lpX d X lpX 30 35 0 36 4 1 L20 0 L65 3 L52 4l65 2 L40 3 10 6 22 0 11 In an article about the time college freshmen use to study each week it was reported that the mean is 68 hours with a standard deviation of 25 hours If 100 freshmen are randomly selected what is the probability that their mean weekly study time exceeds seven hours Suppose in a recent national election 40 of the voters were men If a random sample of 25 voters was selected what is the probability that more than 10 but less than 20 were women A traffic study conducted at one point on an interstate highway shows that vehicle speeds are normally distributed with a mean of 635 miles per hour and a standard deviation of 48 mph a If a vehicle is randomly selected what is the probability that its speed is between 55 and 65 mph b 60 of the speeds in the distribution exceed what value Find the mean and variance of the following probability distribution x 9 1 4 Pxl 3 4 3 Answer Key F F F T d 2119 937 a 5833 b 623mph a 11 b 2829 9959 STA 2122 REVIEW III 1 TrueFalse The width of a con dence interval increases as the sample size decreases everything else held constant It is desirable for the width of a con dence interval to be large A type I error is committed whenever the null hypothesis is incorrectly rejected For an uppertailed hypothesis test if the critical value of z is 233 and the test statistic is 257 the null hypothesis should be accepted 2 Ifa 90 con dence interval for p is 35 45 what is meant by 90 con dence 3 In a random sample of 150 clerical workers 30 exhibit an intense dislike for their jobs Calculate a 94 con dence interval for the proportion of clerical workers who exhibit an intense dislike for their jobs 4 A telephone answering service records the length of each call A random sample of 12 reports yields a mean length of 32 minutes with a standard deviation of 7 minute Calculate a 95 con dence interval for the mean length of phone calls for this answering service 5 A market research rm wishes to determine the mean number of hours families in a particular community watch television per week A random sample of 300 families results in a mean viewing time of 268 hours with a standard deviation of 73 Do you have enough evidence to conclude the mean viewing time in this community exceeds 25 hours Use at 07 6 De ne a Type I and Type II error in terms of problem 5 7 In a random sample of 200 college students 45 had taken Statistics in high school Using 0c 04 do you have enough evidence to conclude the proportion of college students who have not taken Statistics in high school differs from 75 8 Find the pvalue for problem 7 KEY l T F T F 2 In repeated sampling 90 of the intervals constructed will contain p 3 139 261 4 276 364 5 z 427 yes 6 Type I Conclude the mean Viewing time per family in this community is greater than 25 hours when in fact it is less than or equal to 25 hours Type II Conclude the mean Viewing time per family in this community is equal to or less than 25 hours when in fact it is greater than 25 hours 7 z 82 no 4122 STA 2122 Review Questions for Chapter 2 DIRECTIONS When using a formula give formula substitution and answer Round answers to 3 decimal place accuracy when necessary Answer in complete sentences an equation is a sentence I Plant scientists have developed varieties of corn that have increased amounts of the essential amino acid lysine A plant scientist wants to determine whether chicks fed a ration containing corn with increased lysine gain weight faster than those fed a identical ration with normal corn Twenty randomly chosen one day old male chicks were fed the new corn twenty randomly chosen one day old male chicks were fed regular corn The weight gain in grams after 21 days is recorded for each chick Histograms of the data are given for each group 12 LltO dm nmhxm m LltO dm nmhxm Hprbmmquo Weight Gain in Grams Weight Gain in Grams Corn Enriched with Lysine gular Corn 1 For chicks fed a ration with lysine enriched corn the largest proportion of the values lie in the interval 2 How many of the chicks who were fed a ration with regular corn gained more than 350 grams 3 What inference does the plant scientist wish to make II An educator wishes to compare the reading performance of third grade students at two different elementary schools Twenty two third graders from School A and twenty two third graders from School B were randomly chosen The third graders were given the Degree of Reading Power DRP test and their scores were recorded The results are given in the stem and leaf display SCHOOL A B Frequency Stem amp Leaf Frequency 3 844 l 599 3 6 987665 2 257 3 4 8543 3 1345559 7 8 87765431 4 001269 6 l l 5 24 3 Stem width 1000 Each leaf 1 cases l The lowest DPR score recorded is The third grader with the lowest DPR score attends School 2 is the most frequent DPR score recorded for third graders at School B 3 How many third graders had DPR scores 40 or greater 4 What proportion of the third graders at School A have DPR scores less than 30 III For each variable described below indicate whether the measurement is nominal ordinal or interval 1 the number of attempts a person makes before successfully solving a puzz e 2 a football fan s favorite college football team 3 the national ranking of a college basketball team 4 the amount of time required for a student to complete an exam IV The 1 What 2 What 3 What 4 What 5 What 6 What 7 What V what is VI Explain sample is is is is is is is the the the the the the the If n120 observations are 2 2 and 2 mode of this sample median of this sample mean of this sample range of this sample sum of the squared deviations about the mean for this sample sample variance sample standard deviation 2x345 and 2 xi2 2682 the sample standard deviation Dotplots are given or two sample data sets Which data set has the largest variance CE f DO NOT COMPUTE THE VARIAN Agt ATAWAAT T ngggrgT 2 3 4 5 6 7 8 9 Bgt T jAAT T TAWAAF T 2 3 4 5 6 7 8 9 STA 2122 SAMPLE REVIEW CHAPTERS 1 3 not allinclusive 1 True False 7 a The Empirical Rule applies to moundshaped data 7 b A sample is the complete set of observations or measurements of interest to an experimenter 7 c The stemandleaf display is a tool used to graph qualitative data 7 d The union of two events A and B is the event containing all the sample points that are either in event A or event B or both events A and B 7 e In a skewed right distribution the mean is greater than the median 2 Use the sample below to nd the following 680436 mean standard deviation median range mode 3 Identify the following variables as Qualitative or Quantitative The declared major of a college student The cost of a fastfood meal The favorite brand of softdrink of a consumer 4 At one retail store the mean time for a person to complete an application for employment is 245 minutes with standard deviation 39 minutes What is the probability a randomly selected applicant takes longer than 37 minutes to fill out the application 5 A group of faculty and students were surveyed regarding a campus issue their opinions are recorded below Use the following table to answer the following questions OPINION In Favor Opposed No Opinion Faculty 20 34 0 Students 93 70 23 a What proportion of the responses were in opposition to the issue b What proportion of those opposed were faculty c What proportion of the responses were either from students or in favor of the issue d Are the events SStudent and NNo opinion mutually exclusive events Thoroughly justify your answer e Are the events SStudent and NNo opinion independent events Thoroughly justify your answer 6 Suppose 60 ofa group of American citizens is registered to vote and ofthose registered 85 voted in the last Presidential Election What is the probability a randomly selected citizen is both registered to vote and voted in the last Presidential Election KEY Brief answers on the exam remember to show your work 1 T F F T T 2 mean 35 median 5 mode 6 st dev 42 range ll 3 Qual Quan Quan 4 5 a 43 b 33 c 86 d No PSnN 10 i 0 e No PS i PSlN 78 i 100 6 51 at most 11

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