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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
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Page 8 Total Total H l MuitipleChoice 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 pvalne 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 1718 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 519 $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 onesentence 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 2528 §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 [email protected] 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 ernaii 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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 Spring '07
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 Statistics, Standard Deviation, researcher, true proportion

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