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# STATISTICAL METHODS STAT 302

Texas A&M

GPA 3.54

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This 13 page Class Notes was uploaded by Darien Kutch on Wednesday October 21, 2015. The Class Notes belongs to STAT 302 at Texas A&M University taught by Scott Crawford in Fall. Since its upload, it has received 916 views. For similar materials see /class/225748/stat-302-texas-a-m-university in Statistics at Texas A&M University.

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Date Created: 10/21/15

1 4 pointsMy Notes Choose an American farm at random and measure its size in acres Here are the probabilities that the farm chosen falls in several acreage categories Acres lt10 1049 5099 100179 180499 500999 10001999 22000 Probability 012 016 014 012 024 013 006 003 Let A be the event that the farm is less than 50 acres in size and let B be the event that it is 500 acres or more a Find PA Please use 2 decimal places 1 b Find PB Please use 2 decimal places 1 c Find PA Please use 2 decimal places 7 d Find PA or B Please use 2 decimal places H ubmit Answ er ave H39ogress 2 3 pointsMy Notes Here is the probability model for the blood type of a randomly chosen person in the United States Blood Type O A B AB Probability 024 032 013 a What is the probability that a randomly chosen American has type AB blood Please use 2 decimal places b Maria has type B blood She can safely receive blood transfusions from people with blood types 0 and B What is the probability that a randomly chosen American can donate blood to Maria Please use 2 decimal places c What is the probability that a randomly chosen American does not have type 0 blood Please use 2 decimal places ubmit Answ er ave H39ogress 3 1 pointsMy Notes You read that in native Hawaiians the probability of having blood type AB is 1100 1 in 100 This means that C if you pick 99 Hawaiians randomly none of them will have blood type ABEj if you pick 100 Hawaiians randomly exactly 1 of them will have blood type AB C if you pick 100 Hawaiians randomly the fraction of them having blood type AB will be very close to 1100E if you pick 10000 Hawaiians randomly exactly 100 of them will have blood type AB ubmit Answ er ave H39ogress 4 4 pointsMy Notes Use the table of violent deaths below to answer the questions that follow otal a Using the above data what is the probability that the victim was male Please use 4 decimal places b Using the above data what is the conditional probability that the victim was male given that the death was accidental Please use 4 decimal places c Using the above data what is the conditional probability that the death was accidental given that the victim was male Please use 4 decimal places d Using the above data let A be the event that a victim of violent death was a woman and B the event that the death was a suicide The proportion of suicides among violent deaths of women is expressed in probability notation as E PAand BE PAPB E PBAE PAB ubmitAnsw er gave H39ogress l 5 1 pointsMy Notes Twothirds of patients in a drug trial suffered from sever migraines as a side effect Another side effect was impaired vision with 23 of all patients having no impairment 77 having some level of vision impairment What is the probability that a randomly selected patient has no side effects Assume independence and give answer to 3 decimal places Source DugginsJ2009 Test Bank for Baldi and Moore39s Practice of Statistics in the Life Sciencesled Freeman ubmit Answ er ave H39ogress 6 3 pointsMV Notes Fighting probability of fallow deer bucks In Aggressive Behavior JanFeb2007 zoologists investigated the likelihood of fallow deer bucks fighting during mating season During a 270 hour observation period the researchers recorded 205 encounters between two bucks Of these 167 involved one buck clearly initiating the encounter with the other In these 167 initiated encounters the zoologists kept track of whether or not a physical contact fight occurred and whether the initiator ultimately won or lost the encounter The buck that is driven away by the other is considered the loser A summary of the 167 initiated encounters is provided in the accompanying table Suppose we select one of these 167 encounters and note the outcome ght status and winner Initiator Wins No Clear Winner Initiator Loses Totals Fight 26 23 15 64 No Fight 80 12 11 103 Totals 106 35 26 167 Give answers to three decimal places a Given that a ght occurs what is the probability that the initiator wins l b Given no ght what is the probability that the initiator wins I c Are the events quotNo clear winnerquot and quotinitiator losesquot independent E YesE No Source McClave and Sincich 2009 Statistics 1 1th Edition Prentice Hall ubmit Answ er ave H39ogress 7 2 pointsMy Notes In a General Social Survey of Americans in 1991 two variables gender and nding life exciting or dull were measured on 980 individuals The twoway table below summarizes the results Rows Gender Columns Life Is Original Counts Exciting Routine Dull Total Male 213 200 12 425 Female 221 305 29 565 Total 434 505 41 980 Let A randomly chosen person is female Let B randomly chosen person nds life exciting a Find PA l B E 425980E 434980 E 221555E 221434 b Are the events A amp B independent E No because PAl B7 PBj No because PAl B 75 PA E Yes because PA l B PBE Yes because PA l B PA ubmit Answ er gave Fl39ogress 8 4 pointsMy Notes A random sample of 300 men who suffered from lung disease was classi ed as l smoker versus nonsmoker and 2 use of coffee on a typical day The results are of Coffee otal or fewer cupsday or more cupsday otal Suppose we randomly select a man who suffers from lung disease Define the events S individual is a smoker C individual drinks two or more cups of coffee per day a Find PS E 42264 01591E 264 300 08800 G 57300 01900j 42300 01400E None of the above b What is PS and C E 42264 01591E 264 300 08800 E 57 300 01900E 222 300 07400E None of the above c Find PS l C E 222 243 09136E 222 264 08409 C 4257 07368E 264 243 10864E None of the above d Are S and C independent events E No because PC 7E PSE No because PS l C 75 PS E Yes because smoking and coffee use are not relatedE Yes because coffee use and lung disease are not relatedm None of the above ubmit Answ er ave H39ogress 9 3 pointsMy Notes How are the smoking habits of students related to their parents39 smoking Here are data from a large survey of students in eight Arizona high schools Student Student Does Smokes Not Smoke Both parents smoke 5 24 One parent smokes 9 33 Neither parent smokes 2 2l a What is the overall probability that a student smokes Please use 4 decimal places 7 b What is the conditional probability that a student smokes knowing that both parents smoke Please use 4 decimal places l c What is the conditional probability that a student smokes knowing that neither parent smokes Please use 4 decimal places E ubmit Answ er gave H39ogress 10 2 pointsMy Notes a The weather forecast for the weekend is a 32 chance of rain for Saturday and a 42 chance of rain for Sunday If we assume that consecutive days are independent events What is the probability that it rains over the weekend either Saturday or Sunday Please use 3 decimal places b In fact weather on consecutive days depends on similar atmospheric conditions and therefore consecutive days are not independent eventsWith the weather forecast of the previous exercise the probability that it rains over the weekend either Saturday or Sunday is E 06056E 03944 E Because consecutive days are not independent we cannot compute Prain both days with the information given3 03028 ubmit Answ er ave H39ogress 11 1 pointsMy Notes Based on data from the US Center for Health Statistics the death rate for males in the 1524 age bracket is 1144 per 100000 population and the death rate for females is that same bracket is 440 per 100000 population Iftwo males in that age bracket are randomly selected what is the probability that they both survive E 0998E 0002 E 0999E 0001 Source Triola MF 2010 Elementary Statistics 11th Edition AddisonWesley ubmitAnsw er gave H39ogress l 12 1 pointsMy Notes An athlete suspected of having used steroids is given two tests that operate independently of each other Test A has probability 082 of being positive if steroids have been used Test B has probability 069 of being positive if steroids have been used What is the probability that neither test is positive if steroids have been used Remark You should assume that Test A and Test B results are independent E 03202 0124 E 0254j 0566E 0056 ubmit Answ er ave H39ogress 13 2 pointsMy Notes Tree diagrams can organize problems having more than two stages The gure below shows probabilities for a charity calling potential donors by telephone The probabilities given are realistic according to the fundraising rm SCM Associates scmassoccom Each person called is either a recent donor a past donor or a new prospect At the next stage the person called either does or does not pledge to contribute with conditional probabilities that depend on the donor class the person belongs to Finally those who make a pledge either do or don t actually make a contribution 08tg Check Concrihure 01 1 95199 39i Recem w ijxm Mk dam L Not A No Rx 05 No pledge 05 06 I check Contribute I13 Pledge ZR 03 Past 1quot 5 r 7 d 04 No check Nor Gnor Kx 07 quotx No pledge 02 05 gtf Chetk CUnribue 01 av Pledge 39 7 New ref 5 05 No chak N01 pmspazx xxx 5 09 No pledge a What percent of calls result in a contribution Use 1 decimal place b What percent of those who contribute are recent donors Use 1 decimal place ubmit Answ er ave H39ogress 14 4 pointsMy Notes Errors in estimating job costs A construction company employs three sales engineers Engineers 12 and 3 estimated the costs of 30 20 and 50 respectively of alljobs bid on by the company For il23 de ne E i to be the event that a job is estimated by engineer 139 The following probabilities describe the rates at which engineers make serious errors in estimating costs PerrorlE1001 PerrorlEz003 PerrorlE3002 Give answers to three decimal places a If a particular bid results in a serious error in estimating job cost what is the probability that the error was made by engineer 1 l b Ifa particular bid results in a serious error in estimating job cost what is the probability that the error was made by engineer 2 c If a particular bid results in a serious error in estimating job cost what is the probability that the error was made by engineer 3 d Based on the probabilities given parts a c which engineer is most likely responsible for making the serious error E1E2C3 Source McClave and Sincich 2009 Statistics 1 1th Edition Prentice Hall ubmit Answ er ave H39ogress 15 1 pointsMy Notes Enzyme immunoassay tests are used to screen blood specimens for the presence of antibodies to HIV the virus that causes AIDS Antibodies indicate the presence of the virus The test is quite accurate but is not always correct Here are approximate probabilities of positive and negative test results when the blood tested does and does not actually contain antibodies to HIV est est absent Suppose that 1 ofa large population carries antibodies to HIV in its blood Draw a tree diagram with this information and use it to answer the following question What is the probability that the test is positive for a randomly chosen person from this population Please use 4 decimal places ubmit Answ er ave H39ogress 16 1 pointsMy Notes A factory has three machines that all manufacture the same engine pa1t From long historical records the company has determined that the first machine produces 4 defectives the second machine produces 6 defectives and the third machine produces 1 defectives Suppose also that the first machine produces 30 the second machine 20 and the third machine 50 of the engine pa1ts An engine pa1t is selected at random Ifthe part is defective What is the probability that was produced by the first machine Please use 3 decimals ubmit Answ er gave H39ogress 17 1 pointsMy Notes Sport utility vehicles SUVs are generally considered to be more prone to roll over than cars In the USA in 1997 240 of all fatalities involved a rollover In addition given that the fatality involved a rollover 158 of all fatalities involved SUVs Furthermore given that the fatality did not involve a rollover 56 of all fatalities involved SUVs Suppose that a fatality involved an SUV calculate the probability that the fatality involved a rollover Please use 3 decimal places ubmit Answer gave H39ogress 18 1 pointsMy Notes Treating Brain Cancer According to the Children39s Oncology Group Research Data Center at the University of Florida 20 of children with neuroblastoma a form of brain cancer undergo surgery rather than the traditional treatment of chemotherapy or radiation The surgery is successful in curing the disease 95 of the time ExploreSpring 2001 Consider a child diagnosed with neuroblastoma What are the chances that the child undergoes surgery and is cured Give answer to two decimal places Source McClave and Sincich 2009 Statistics 11th Edition Prentice Hall ubmit Answ er gave H39ogress 19 2 pointsMy Notes Pharmaceutical companies advertise for the birth control pill an annual efficacy of 993 in preventing pregnancy However under typical use the real efficacy is only about 95 That is 5 of women taking the pill for a year will experience an unplanned pregnancy that year The difference between these two rates is that the real world is not perfect for example a woman might get sick or forget to take the pill one day or she might be prescribed antibiotics which interfere with hormonal metabolism If a sexually active woman takes the pill for the four years she is in college what is the chance that she will become pregnant at least once Assume that the chance of pregnancy for each year is independent a Give your answer using the theoretical efficacy of the pill Please use 4 decimal places b Give your answer using the real efficacy of the pill Please use 4 decimal places ubmit Answ er gave H39ogress 20 1 pointsMy Notes Part of America39s military success in the rst Gulf War was due to the high performance of Raytheon Corporation39s Patriot Missile SystemThe Patriot missile was designed to intercept missiles and destroy them in the air The missile s rate of successful intercepts of Iraqi Scud missiles aimed at Israel and Saudi Arabia surprised even its makers At a speech made at Raytheon s headquarters in Andover Massachusetts on February 15 1991 George Bush stated that 41 out of 42 incoming missiles were intercepted by the Patriot system From publicly available sources the following can be inferred about the Patriot system quotThere is a 99 chance that the system s radar will detect an incoming enemy missile such as the Scud Once the missile is detected a Patriot missile is red and has a 985 chance of exploding close enough to the incoming missile so that its fragments will damage the incoming missile If this happens there is a 65 chance that the incoming missile will explode in the air and thus cause no damagequot Calculate the probability that an incoming missile will be totally destroyed in the air by a Patriot missile Please use 3 decimals ubmit Answ er ave H39ogress ubmit Assignment gave Assignment H39ogress Home My Assignments WebAssign 40 19972003 by North Carolina State UniversityPortions 20032011 by Advanced Instructional Systems Inc All rights reserved

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