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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
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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 ii.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(AB) Total {12) 5. Which of the following are true statements?
1. The pvalne is the probability that the nnli hypothesis is true.
ii. A small pvalue 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 PValue 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 retellsa 2; Use the followin information to answer uestlons 1516 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 emaii messages
are spare. A random sample of 14 ewmail messages is selected. What is the probability that at most 12 of the 14 email 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 2223 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 pvaiue. ’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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 Statistics

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