Stats exam 2 - Name Red Id STAT 119 EXAM TWO April 17, 2008...

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Unformatted text preview: Name Red Id STAT 119 EXAM TWO April 17, 2008 Form H You have 75 minutes to complete this exam. Mark your answers neatly on the exam and be sure to Show all your work. Please Ioond your answers to four digits after the (feeimal. 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 To£al i’age 2 Totai Page 3 Total Page 4 Toial Page 5 Total Page 6 Total Page 7 Total Page 8 Total Total H l Muitiple-Choice Questions are worth 3 points: 1. A researcher wants to determine whether drinking red wine is better at reducing blood pressure than drinking white wine. Two studies are designed. In the first, 200 people who do not usually drink wine are randomiy selected. Haif the subjects are asked to drink one giass of red wine daily for 6 months, the remaining subjects are asked to drink one giass of white wine daiiy for 6 months. Biood 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 oniy white wine are seiected. The biood pressures of the 200 subjects are taken. Which of the foilowing is true? A. Both studies are observational studies. __ 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. D. Both studies are experiments 2.. A large monkey house at a 2.00 has a population of 950 monkeys and i2% 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 sampie proprtion for this sample? The sample size is greater than 10% of the population. . The sample was not randomly seiected . The population is not normally distributed. . np < 10 . None of the conditions were vioiated Answer 3. Suppose you win a contest, and as a prize are allowed to draw. while blindfolded, 2 biiis from a container. Inside the container are seven $1 doliar bilis, four $10 doliar bitis, and eight $20 doliar biils. What is the probability of drawing at least 1 $20 dollar bili? A. 0.515 a. 0.257 (3. 0.42i @ 0.678 Answer 4. Which of the following statements is true? A. The sampiing distribution of the sampie proportion ( f9 ) is normai with pmS B. The standard deviation of a sample proportion (0 f, ) increases as the sample size increases 9 The standard deviation of a sampie mean (0 E ) decreases as the sample size 1ncreases D. The sampling distribution of the sample mean (X ) is always normal if n2 10 Total (12) 5. 39% of new model cars have a built in DVD piayer, 21% have a GPS navigation system, and 47% have at least one of these two features. What is the probability that a new modei car has both of these featares? @ 0.13 B. 0.08 C. 0.26 D. 0.0819 E. 0.6 Answer 6. A medical researcher estimates the percentage of children who are exposed to lead based paint, adding that he beiieves his estimate has a margin of error of about 3% meaning A. He believes that 97% of the population faEis under his estimate 13. He believes the true proportion is within $1.592: 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 13% of his estimate Answer: 7. The Central Limit Theorem tells us that: A. The mean of the distribution of sample means is less than the mean of the parent population. B. The standard deviation of the distribution of sample means is the same as the standard deviation of the popniation. : The shape of the sampling distribution of the sampie mean is approximately normal for large n. D. The shapes of 2111 sampling distributions of sample means are normally distributed. 8. Which of the following is ALWAYS true? A. P(A m B) = P(A)P(B) B. P(AUB) m P(A)+P(B) 3 mm B) = m P(A) . P(A) —1= MAC) None of the Above Answer: Total (12) 9. Which of the following are true statements? 1. The p—value is the probability that the null hypothesis is true. 11. To reject the nuil hypothesis, it rnust be false. 111. A small p-valne implies strong evidence against the null hypothesis. A. lonly B. 11 only S C} 111 only . Two of the above are true statements. E. None of the above are true statements. Answer: 10. hich of the following statements about confidence intervals is INCORRECT? If we increase both the sample size and the confidence level the confidence interval will be unchanged. B. if we keep the sample size fixed, the confidence interval gets wider as we increase the confidence level. C. A confidence interval for a population proportion always contains the sample proportion. D. If we keep the confidence level fixed, the confidence interval gets narrower as we increase the sarnple size. ll. in testing the hypotheses H9 : p 2* 0.56 Ha: p < 0.56 The p—value is found to be .0712, with a sample proportion of 0.52. Which of the fol'iowing statements is true? A. The probability of observing a sample proportion larger than 0.52 from a population with true proportion 0.56 is .07l2 B. Since the p—value is larger than the difference between 0.56 and 0.52 we shouid reject the null hypothesis. C. The probability of observing a sample proportion smelter than 0.56 from a population with true proportion 0.52 is .0712. The probability of observing a sampie proportion smailer than 0.52 from a population with true proportion 0.56 is .0712. E. None of the above statements is correct Answer 12. Which of the following is tree of an observational study? It can look forward or backward in time Biinding can he used to reduce bias. The subjects can run through the test twice, acting as their own “Matched Pair”. A nurnher of different treatment levels can be applied to the subjects. All of the above are true for an observational study Total {12) wrong 13. Accorclirig to the State Department, only twenty—seven percent of Americans carry a valid passport. Suppose we take a random sample of 11 Americans. Which of the foilowing best describes the distribution of X=number of Americans that carry a valid passport? A. X ~ AN(ll, 0.27) B X ~ AN(2.97, 1.472) X ~ N997, 1.5l72) X~B(2.97, 1.472) X ~ 13(11, 0.27) C. D Answer 14. An unethicai statistician performs a hypothesis test on the effects of a drug on relief of headaches. Hypothesis test results from the drug trials yieid a PdValue of 0. l5 for the proportion of headaches relieved reiative to the placebo. Determined to publish that the headache relief results are significant the statistician chooses the aipha level after the test is performed. What alpha levei will he select? A. 0.10 B. 0.05 -j' 0.20 D. 0.01 Answer \‘ W W I Use the followin information to answer uestions 1546 9 oints : f w” ° l A; “a” 9; & It is known that 35% of employees have an individual retirement plan (iRA). Given an employee .. ,% we is under 40 years of age, they have a 28% chance of having an individual retirement plan (IRA). $5 a 33 r Currently 56% 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 ‘RA? et a o a“) r: eta} we eéssitts’) Answer: f; ’ 16. (5 points) If a randomly selected employee has an ERA, what is the probability the employee is under 40 years old? eta; Answer: a Total (20) H 5 Use the following information to answer Questions 17-18 19 gointst: Nine percent of workers in the Unites States use gublic transportation to get to work. A random sample of 310 workers are selected and asked if they use pubiic transportation to get to work. 17. (3 points) Describe the sampling distribution of the number of workers (in the sample of 310) that say they use public transportation to et to work. Use the appropriate notation. X A! 3% fi § {3% Answer: i9. (16 points) A government study ciairned that 60% of Americans agree that oil expioration in our national parks is necessary. In a survey of 1765 Americans, 1085 said they agree that oil exploration in our national parks is necessary. is this sufficient evidence to reject the claim? I. (3 points) State the appropriate null and alternative hypotheses. iie: 3:“ III. (3 points) Calculate the corresponding pmvalue. Eevettw a; 2,... ?{er 5-19 $24 Jest} *3 as W. (3 points) Make a statistical decision using level of significaace of 0.05. Justify your decision. Q“ a? Q; era “7} « a? V. (3 points) Interpret your decision in the context of the problem. 20. (5 points) A iocal surf shop has 19 surfboards availabie for rental: 6 shortboards and 13 longboards. Two friends (who know nothing about surfing) decide to rent boards for the day. The friends randomly select two of the 19 available surfboards. Construct the probabiiity distribution for Xm the number of shortboards seiecteti. Show ail work. Use the foilowing information to answer guestions 21 ~24 $15 gointslz In a study of food safety, it was found that 32 of a random sample of 255 broiler chickens were infected with Sairnonelia. 2}. (2 points) the conditions for constructing a cnfid fgifi g. Efi} £§ r g. 22. (6 points) Construct a 98% confidence interval for the proportion of broiler chickens infected with Salmonena _, éi e intnal satisfied? Expla' . net: 5?“- Answer: ’ ‘ 23. (3 points) Give a one-sentence interpretation of the confidence interval. within 3% with 98% confidence? no t 1’3 __ ,. .s 5 i $1, H 7 Male: Egg? fig}: *éi fleas}: ea. Use the followiag to answer Questions 25-28 §17 points;: A survey of college freshmen found that the probability a freshman lives in a campus residence hail (event A) is 0.57 and the probability that a college freshman participates in a campus meal program (event B) is 0.61. The probability a randomly selected college freshman lives on campus or participates in a meal program is 0.72 25. ( 4 points) What is the probability that a randomly selected college freshman lives on campus and participates in a campus meal program? tie e@ s; eta; «t are w» arm a :memafi «El :2“ egfit serge Answer: 2’ as» g W 26. (4 points) Fill in all 4 areas of the Venn diagram below with the appropriate probability 27. (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? W 28. (4 points) Are living on campus and having a meal plan independent? Justify your answer using probabilities calcuiated above. N fig, f3 % gfa fi § § slaliml geltiil see all Total: (17) 29. (6 points) A communications monitoring company reports that 84% of e—mail messages are spam. A random sample of i2 e-rnaii messages is seiected. What is the probability that at most 10 of the i2 e—rnaii messages are spam? gifigieés: is” ‘flfifig iig 30. (6 points) In a certain conservative precinct, 81% of the voters are registered Republicans. What is the probability that in a random sample of 75 voters from this precinct more than 73% would vote for the Republican candidate? $5 ié a .:%%§ .1: Wis ? 3”“ Answer: Use the following information to answer Questions 31*33 115 points}: Prices of women’s athletic shoes are skewed right with a mean of $84.35 and a standard deviation of $19.05. A random sample of 70 pairs of women‘s athietic shoes is selected. 3i. (3 points) Describe the sampling distribution of the average price of women’s athletic shoes for the sample of 70 pairs of shoes. Use the appropriate notation. 32. (6 points) What is the probability that the verage price of the sample of 70 pairs of shoes falls between $78 and $86? 33. (6 points) What is the value of the sample mean price of women’s athletic shoes such that only 4% of the sampie means fail above this value? Totai (2’7) ...
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This note was uploaded on 05/04/2008 for the course STAT 119 taught by Professor Helen during the Spring '07 term at San Diego State.

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Stats exam 2 - Name Red Id STAT 119 EXAM TWO April 17, 2008...

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