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Exam2G - Name Red It STAT 119 EXAM TWO April E7 2008 Form G...

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Unformatted text preview: Name Red It} STAT 119 EXAM TWO April E7, 2008 Form G You have 75 minutes to complete this exam. Mark your answers neatly on the exam and be sure to Show all your work. Please round your answers to four digits after the decimal. Make sure to put your final answers neatly within the answer boxes (when provided). Please CIRCLE the correct answer and use CAPITAL LETTERS in the space provided for the multiple choice. BE CAREFUL! GOOD LUCK! Page 1 Total Page 2 Total Page 3 Total Page 4 Total Page 5 Total Page 6 Total Page 7 Total Page 8 Total Total G l Multiple‘Choice Questions are worth 3 points: i. 39% of new modei cars have a built in DVD player, 21% have a GPS navigation system, and 47% have at least orte of these two features. What is the probability that a new model car has both of these features? A. 0.08 B. 0.26 C. 00819 i). 0.6 @013 Answer 2. A medical researcher estimates the percentage of children who are exposed to lead based paint, adding that he believes his estimate has a margin of error of about 3% meaning A. He believes the true proportion is within i-i.5% of his estimate He is making this up because he is not really sure what the true proportion is. He beiieves the true proportion is within :3% of his estimate D. He believes that 97% of the popuiation falls under his estimate Answer: 3. The Centrai Limit Theorem tells us that: A. The standard deviation of the distribution of sampie means is the same as the standard deviation of the population. B. The shape of the sampiirag distribution of the sample mean is approximately normal for large n. C. The shapes of all sampling distributions of sample means are normally distributed. D. The mean of the distribution of sample means is less than the mean of the parent population. Answer 4. Which of the foilowing is ALWAYS true? A. P(A U B) : P(A) + P(B) _ P(A n B) " PtA) C. Pot) —i m P(AC) D. P(Afl B) m P(A)P(B) @ None of the Above a. P(A|B) Total {12) 5. Which of the following are true statements? 1. The p-valne is the probability that the nnli hypothesis is true. ii. A small p-value implies strong evidence against the null hypothesis. 111. To reject the null hypothesis, it must be false. A. i only 11 only . ill only D. Two of the above are true statements. E. None of the above are true statements. 6. Which of the following statements about confidence intervals is INCORRECT? A. If we keep the sample size fixed, the confidence interval gets wider as we increase the confidence levei. B. A confidence interval for a population proportion always contains the sample proportion. C. If we keep the confidence level fixed, the confidence interval gets narrower as we increase the sample size. {D If we increase both the sarnple size and the confidence level the confidence intervai will be unchanged. Answer: 7. In testing the hypotheses H0 : p = 0.56 Ha : p < 0.56 The p—vaiue is found to be .0712, with a sample proportion of 0.52. Which of the following statements is true? A. Since the p—vaiue is larger than the difference between 0.56 and 0.52 we should reject the null hypothesis. B. The probability of observing a sample proportion smaller than 0.56 from a population with true proportion 0.52 is .0712. @ The probability of observing a sample proportion srnalier than 0.52 from a " population with true proportion 0.56 is .0712. D. The probability of observing a sample proportion larger than 0.52 from a population with true proportion 0.56 is .0712 E. None of the above statements is correct 8. Suppose you win a contest, and as a prize are allowed to draw, while blindfolded, 2 biils from a container. Inside the container are seven $1 dollar bills, four $l0 dollar bills, and eight $20 dollar bills. What is the probability of drawing at least 1 $20 doilar bill? A. 0.515 B. 0.421 C. 0.678 D. 0.257 Answer Total (12) 9. According to the State Department, only twentymseven percent of Americans carry a vaiid passport. Suppose we take a random sample of it Americans. Which of the foliowing best describes the distribution of X=nurnber of Americans that carry a valid passport? A. X ~ N(2.97, 1.472) B. X~B(2.97, 1.472) X ~ B01, 9.27) . X ~ AN(11,0.27) E. X ~ AN(2.97, 1.472) 5"} Answer w 10. Which of the following is true of an observationai study? A. Blinding can be used to reduce bias. B. The subjects can run through the test twice, acting as their own “Matched Pair”. C. A number of different treatment levels can be applied to the subjects. It can look forward or backward in time B. Ail of the above are true for an observational study it. An unethicai statistician performs a hypothesis test on the effects of a drug on relief of headaches. Hypothesis test results from the drug trials yield a P-Value of 0.15 for the proportion of headaches relieved relative to the piacebo. Determined to publish that the headache relief results are significant the statistician chooses the alpha level after the test is performed. What alpha level wiil he seiect? A. 0.015 corn 110.10 Answer 12. A researcher wants to determine whether drinking red wine is better at reducing b'iood pressure than drinking white wine. Two studies are designed. In the first, 200 people who do not usually drink wine are randomiy selected. Half the subjects are asked to drink one glass of red wine daily for 6 months, the remaining subjects are asked to drink one glass of white wine daiiy for 6 months. Blood pressures of the subjects were taken before and after the 6 month period. In the second study, 100 subjects who drink only red wine and 100 subjects who drink only white wine are selected. The blood pressures of the 200 subjects are taken. Which of the following is true? A. The first study is an observational study, and the second is an experiment. The first study is an experiment, and the second study is an observational study. . Both studies are experiments D. Both studies are observational studies. Total (12) 13, A large monkey house at a zoo has a popniation of 950 monkeys and l2% of them are overweight. A sample of 200 randomly selected monkeys was taken and 8% of them were overweight. Why is it inappropriate to use sampling distribution of the sample proportion for this sample? A. The sample was not randomly selected B. The population is not normally distributed. C. np < 10 ® The sample size is greater than 10% of the population. E. None of the conditions were violated Answer 14. Which of the following statements is true? A. The standard deviation of a sample proportion (0 i2 ) increases as the sample size increases The standard deviation of a sample mean (0 3 ) decreases as the sample Size increases The sampling distribution of the sample mean {if ) is always normal if n 210 The sampling distribution of the sample proportion ( g5 ) is normal with p=.5 no Answer & W N retells-a 2; Use the followin information to answer uestlons 15-16 9 oints : _ It is known that 32% of employees have an individual retirement plan (IRA). Given an employee is under 40 years of age, they have a 21% chance of having an individual retirement plan (IRA). Currently 57% of the workforce is under 40 years of age. 15. (4 points) What is the probability a randomly selected employee is under 40 and has an ‘R We am steam; Answer: iifi? j: ‘iifi? l6. (5 points) If a randomly selected employee has an IRA, what is the probability the employee is under 40 years old? Total (15) £37. (6 points) In a certain conservative precitict, 84% of the voters are registered Republicans. What is the probability that in a random sampie of 85 voters from this precinct more than 76% woaid vote for the Repuhiican candidate? at Answer: ~fi§r¥§ ; 18. (6 points) A communications monitoring company reports that 89% of e-maii messages are spare. A random sample of 14 ewmail messages is selected. What is the probability that at most 12 of the 14 e-mail messages are spanfi the it? a: term t3 la i. see? Use the following information to answer Questions 19~21 (is pointsgz Prices of women’s athletic shoes are skewed right with a mean of $74.25 and a standard deviation of $16.45. A random sample of 40 pairs of women’s athletic shoes is selected. 19. (3 points) Describe the sampling distribution of the average price of women’s athletic shoes for the sample of 40 pairs of shoes. Use the appropriate notation. i... es: Mi :- Mm Answer: X it; figsf {Wily Eg‘$§§a 3‘ J; 20. (6 points) What is the probability that the average price of the sampie of 40 pairs of shoes falls between $68 and $75? B H sari as" 21. (6 points) What is the vahte of the sample mean price of women” s athletic shoes such that only 7% of the sample means fall above this value? "1:; 2?? g 93% § gig? é; Total (27) G 6 Use the foilowing information to answer Questions 22-23 19 pointsl: Six percent of workers in the Unites States use public transportation to get to work. A random sample of 270 workers are seiected and asked if they use pubiic transportation to get to work. 22. (3 points) Describe the sampling distribution of the number of workers (in the sample of 270) that say they use public transportation to get to work. Use the appropriate .. gait notation. X w E i :3 .3 Q é Answer: 23. (6 points) Find the probability that at least 12 of the 270 workers say that they use public transportation to get to work. fixefl E 24. (16 points) A government study claimed that 60% of Americans agree that oil exploration in our national parks is necessary. In a survey of 1625 Americans, 1025 said they agree that oil exploration in our national parks is necessary. Is this sufficient evidence to reject the ciaim? i. (3 points) State the appropriate null and alternative hypotheses. “its: $Lr§ ifs? rat it. (4 points) Calculate the test statistic $1: né‘zgg’“ 5?? S3 III. (3 points) Calculate the corresponding p-vaiue. ’Pygfigm h; 2995??? 33*}; g; l vs?) your; IV. (3 points) Make a statistical decision using level of significance of 0.05. Justify your decision. ?, sfiiifiéw { pg‘ & .siro d as? V. (3 points) Interpret your decision in the context of the problem. 25. (5 points) A local surf shop has 19 surfboards available for rental: 11 shonboards and 8 longboards. Two friends (who know nothing about surfing) decide to rent boards for the day. The friends randomiy select two of the £9 availabie surf boards. Construct the probabiiity distribution for X: the number of shortboards selected. Show all work. $33“ ${X§Q§:§xifié 5 ft is” { iii/fig { on E f 331x 3%; .. M Use the followin information to answer uestmn «29 15 oints : 5’53 gg In a study of food safety, it was found that 58 of a random sampie of 365 broiler chickens were infected with Salmoneiia. 26. (2 points) Are the conditions for constructing a confidence interval satisfied? Explain. 3» §£§ infected with Salmonella. «ism i 3% been :i Ems Am... we; w“? 28. (3 points) Give a one—sentence interpretation of the confidence interval. 29. (4 points) How large a sample shouid be taken in order to estimate the proportion to within 2% with 95% confidence? .: his 3‘ §y n r: it fie? _, _ m V m 3m; Answer: Total 120} G a {$1111 ? @E Use the following to answer Questions 30- 33 117 points): A survey of college freshmen found that the probability a freshman lives 1n a campus residence hall (event A) 15 0 58 and the probability that a college freshman participates in a campus meal program (event B} 13 0.65 The probability a randomly selected college freshman lives on campus or participates in a meal program is 0 79 3G. ( 4 points) What 15 the probability that a randomly selected college freshman lives on campus and participates in a campus meal program” m 11:1 1 a} am 1:: 1111 ea “1 11a 1 $1 £11111“ .1: 31. (4 points) Fill 111 all 4 areas of the Venn diagram below with the approiiate probability 32. (5 points) If a randomly selected college freshman lives in a campus residence hall, what is the probability that the freshman participates in a campus meal program? Answer: 33 (4 points) Are living on campus and having a meal plan independent? Justify your answer using probabilities calculated above a :11 We Total: (17) ...
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