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Unformatted text preview: Name Rec} Id STAT 119 EXAM TWO April 17, 2008
Form F 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 LUCKE Page 1 Total
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Page 8 Total Totai F l MultipleChoice Questions are worth 3 points:
1. Which of the following are true statements? 1. The pvalue is the probability that the null hypothesis is true.
II. A small p—value implies strong evidence against the null hypothesis. III. To reject the nail hypothesis, it must be false. A. I only ; II only
111 only
Two of the above are true statements.
None of the above are true statements, D.
E. Answer: 2. Which of the following statements about confidence intervals is INCORRECT?
A. A conﬁdence interval for a population proportion always contains the sample proportion.
B. if we keep the conﬁdence level fixed, the conﬁdence interval gets narrower as we increase the sample size.
C. t we increase both the sample size and the conﬁdence level the confidence interval will he unchanged.
D. if we keep the sample size ﬁxed, the confidence interval gets wider as we increase the conﬁdence level. 3. 39% of new model cars have a built in DVD player, 21% have a GPS navigation system,
and 47% have at least one of these two features. What is the probability that a new model car has both of these features? A. 0.26 B. 0.08 C. 0.13 D. 0.0819 E. 0.6 Answer 4. Which of the following is ALWAYS true? A.HME=E%%@ B.Hm—MPmﬁ C. P(A m B) m P(A)P(B)
D, P(AU B) = P(A) ~€~ 13(3)
® None of the Above Total (12) 5. In testing the hypotheses H0 : p = 0.56 Ha : p < 0.56 The p—vaiue is found to be .0712, with a sampie proportion of 0.52. Which of the
following statements is true?
A. The probabiiity of observing a sampie proportion smalier than 0.56 from a
population with true proportion 0.52 is .0712.
{Q The probability of observing a sampie proportion smaller than 0.52 from a
popuiation with true proportion 0.56 is .0712.
C. The probability of observing a sample proportion larger than 0.52 from a
population with true proportion 0.56 is .0712
D. Since the p—value .is Earger than the difference between 0.56 and 0.52 we should
reject the nuil hypothesis.
E. None of the above statements is correct Answer 6. According to the State Department, only twentyseven percent of Americans carry a valid
passport. Suppose we take a random sample of 11 Americans. Which of the foiiowing
best escribes the distribution of X=nurnber of Americans that carry a vaiid passport? é X ~ B(i1, 0.27)
B. X ~ AN(11,0.27)
C. X ~ AN(2.97, 1.472)
D. X ~ N(2.97. 1.472)
E. X~B(2.97, 1.472) 7. Which of the following is true of an observational study?
A. The subjects can run through the test twice, acting as their own “Matched Pair”. B. A number of different treatment ievels can be appiied to the subjects.
it can look forward or backward in time D. Biinding can be used to reduce bias. B. All of the above are true for an observational study Answer 8. An unethical statistician performs a hypothesis test on the effects of a drug on reiief of
headaches. Hypothesis test results from the drug triais yield a P~Vaiue of 0.15 for the
proportion of headaches relieved relative to the ptacebo. Determined to publish that the
headache relief results are signiﬁcant the statistician chooses the alpha ievel after the test
is performed. What aipha ievei wiEi he select? 0.20 B_ 001 c. 0.10 D. 0.015 Total __(12) 9. 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 randomly selected. Half the subjects are asked to drinit one
giass of red wine daily for 6 months, the remaining subjects are asked to drink one glass
of white wine daily 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 foilowing is true? @ The ﬁrst study is an experiment, and the second study is an observational study.
B. Both studies are experiments
C. Both studies are observationai studies.
D. The ﬁrst study is an observational study, and the second is an experiment. 10. A large monkey house at a zoo has a population of 950 monkeys and 12% of them are
overweight. A sample of 200 randomly seiected 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 population is not normally distributed. B. np < 10 The sample size is greater than 10% of the population.
D. The sample was not randomly selected
E. None of the conditions were violated ll. Suppose you win a contest, and as a prize are aliowed to draw, whiie blindfolded, 2 biils
from a container. Inside the container are seven 31 dollar bills, four $10 dollar bills, and
eight $20 dollar bills. What is the probability of drawing at least 1 $20 dollar biil? A. 6.421 C. 0.257 D. 0.515 Answer SM 2% it} S ~
5 iii? .12. Which of the following statements is true?
The standard deviation of a sample mean (0}) decreases as the sample size increases The sampling distribution of the sampie mean (3? ) is always normal if n 2 10
The sampling distribution of the sample proportion ( f) ) is norrnai with p=.5 B.
C.
D. The standard deviation of a sampie proportion (O f, ) increases as the sample size increases Answer Total (3.2) 13. A medical researcher estimates the percentage of chiidren who are exposed to Eead based
paint, adding that he beiieves his estimate has a margin of error of about 3% meaning
A. He is making this up because he is not really sure what the true proportion is.
(3 He believes the true proportion is within 13% of his estimate
C. He believes that 97% of the population fails under his estimate
D. He believes the true proportion is within :1.5% of his estimate i4. The Central Limit Theorem tells us that:
"j: The shape of the sampling distribution of the sample mean is approximately . normal for iarge n.
B. The shapes of all sampling distributions of sample means are normaiiy distributed.
C. The mean of the distribution of sample means is less than the mean of the parent population.
D. The standard deviation of the distribution of sample means is the same as the standard deviation of the population. Use the followin information to answer uestions 1516 9 oints :
Eight percent of workers in the Unites States use public transportation to get to work. A random sample of 320 workers are selected and asked if they use pubiic transportation to get to work. 15. (3 points) Describe the sampling distribution of the number of workers (in the sampte of
320) that say they use public transportation to get to work. Use the appropriate notation. X it; 35 318. dig) ﬂag“? I: 1&3
... ig’iﬂgé
a}; W _. it 16. (6 points) Find the probability that at least 20 of the 320 workers say that they use public
transportation to get to work. Xa3® Answer: Totai (IS) l7. (6 points) A communications monitoring company reports that 83% of emaii messages
are spam. A random sarnple of 11 e—mail messages is selected. What is the probabiiity
that at most 9 of the 11 email messages are spam? agesaaziw meats”) 18. (6 points) In a certain conservative precinct, 79% of the voters are registered
Repubiicans. What is the probability that in a random sample of 65 voters from this
precinct more than 71% would vote for the Repab .ican candidate? i
dida'i’g a 335%“? “MW .. .é XIETWW ._... ,.:== ,= ,7 I. 3 ate? ,. trio ...; awe Use the foliowin information to answer uestions 1921 15 oints :
Prices of women’s athletic shoes are skewed right with a mean of. $82.95 and a standard deviation of $18.15. A random sampte of 60 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 60 pairs of shoes. Use the appropriate notation.
$5 if“ ...... g, 3 a “‘3 2. .... til: ......
Answer: X WN {33.9}? 333L331? ”X 5% 20. (6 points) What is the probability that the average price of the sampie of 60 pairs of shoes
falls between $77 and $85? Figsa <3? et’0 ...: a a  e a
teat? ti; Answer; swig _ .2... ﬂ... ast sees 21. (6 points) What is the value of the sampie mean price of women’s athletic shoes such that
oniy 9% of the sample means fall above this value?
i. s a Total (27) Wham “l v z: i a. it at: :2 Use the followin informatieﬁ t 7' .
It is known that 31% of employees have an individuai retirement plan (IRA). Given as employee is under 40 years of age, they have a 26% chance of having an individuai retirement plan (IRA). Currently 54% of the workforce is under 40 years of age.
22. (4 points) What is the probability a randomly selected employee is under 40 and has an M w eteEttétei Answer: i €55? ﬁg 3:; 23. (5 points) If a randomiy selected employee has an ERA, what is the probability the
employee is under 40 years oid‘? W l 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 1455 Americans, 895 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. HQ: are Mai 4? at it. (4 points) Calculate the test statistic Answer: 9 , g 3 HI. (3 points) Caiculate the corresponding p~value. 5’
W 5e“? t a i ?” easier, 3 L wet Me} a a: IV. (3 points) Make a statisticai decision using level of signiﬁcance of 0.05. Eustify your
d6C1SlOﬂ. ?i V & ii 3 E 32, g g .. {ﬁﬁﬁé
, Q3 are ‘7} « e3? V. (3 points) interpret your decision in the context of the problem. gapaitee arse ﬁWotat (25)
. _ , & 25. (5 points) A local surf shop has 19 surfboards availabie for rental: l3 shortboards and 6
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
probability distribution for X: the number of shortboards seiected. Show all work. Use the foilowin information to answer uestiens 26 .
In a study of food safety, it was found that 64 of a random sample of £95 broiier chickens were infected with Salmonella.
26. (2 points) Are the conditions for constructing a conﬁdence interval satisﬁed? Expiain. g. mgggij énﬁe?i§
n% 335$“
33% Q gnﬁ § ?a§nia§e§m 27. (6 points) Construct a 99% conﬁdence interval for the proportion of broiler chickens
infected with Salmonella.   ' "  '   Answer: ’ @ﬁégy ‘3 ’ gégg 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 99% conﬁdence? as: {anon {ammo4m} .3 5%? Mai Answer: a E’é % Total (20) F 8 ?iﬁ'}: ‘ SQ fig} 3 s g §§ Use the following to answer Questions 3033 [17 points): A survey of coliege freshmen found that the probability a freshman lives in a campus residence
hall {event A) is 0.59 and the probability that a college freshman participates in a campus meai
program (event B) is 0.64. The probability a randomly selected college freshman lives on campus or participates in a meal program is 0.78
30. (4 points) What is the probability that a randomly selected college freshman lives on
campus and participates in a campus meal program? Answer: $3 We f3 5? 31. {4 points) Fill in all 4 areas of the Venn diagram below with the appropriate probability 32. (5 points) If a randomly selected coilege freshman lives in a campus residence hall, what
is the probability that the freshman participates in a campus meal program? grmwisiw sf am. a a am as} Total: (17) ...
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 Spring '07
 Helen
 Statistics

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