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AP/ACC Statistics
Unit 5 AP Test Review—Multiple Choice
Choose the response that best answers the question or completes the statement.
1. Which of the following is an incorrect statement?
(A) The sampling distribution of 𝑥̅ has mean equal to the
population mean 𝜇 even if the population is not normally
distributed.
(B) The sampling distribution of 𝑥̅ has standard deviation
𝜎
even if the population is not normally distributed.
√𝑛
(C) The sampling distribution of 𝑥̅ is normal if the
population has a normal distribution.
(D) When n is large, the sampling distribution of 𝑥̅ is
approximately normal even if the population is not
normally distributed.
(E) The larger the value of the sample size n, the closer the
standard deviation of the sampling distribution of 𝑥̅ is to
the standard deviation of the population.
2. Which of the following is a true statement?
(A) The sampling distribution of 𝑝̂ has a mean equal to the
population proportion 𝑝.
(B) The sampling distribution of 𝑝̂ has a standard deviation
(B) The mean gets closer to the population mean, the
standard deviation becomes smaller, and the shape
becomes more skewed left.
(C) The mean gets closer to the population mean, the
standard deviation stays the same, and the shape becomes
closer to normal.
(D) The mean gets closer to the population mean, the
standard deviation becomes smaller, and the shape
becomes closer to normal.
(E) The mean stays the same, the standard deviation becomes
smaller, and the shape becomes closer to normal.
5. Suppose that 35% of all business executives are willing
to switch companies if offered a higher salary. If a
headhunter randomly contacts an SRS of 100 executives,
what is the probability that over 40% will be willing to
switch companies if offered a higher salary?
(A) .1469
(B) .1977
(C) .4207
(D) .8023
(E) .8531
equal to √𝑛𝑝(1 − 𝑝).
(C) The sampling distribution of 𝑝̂ has a standard deviation
which becomes larger as the sample size becomes larger.
(D) The sampling distribution of 𝑝̂ is considered close to
normal provided that 𝑛 > 30.
(E) The sampling distribution of 𝑝̂ is always close to
normal.
6. The average outstanding bill for delinquent customer
accounts for a national department store chain is $187.50
with a standard deviation of $54.50. In a simple random
sample of 50 delinquent accounts, what is the probability
that the mean outstanding bill is over $200?
(A) .0526
(B) .0667
(C) .4090
(D) .5910
(E) .9474
3. In a school of 2500 students, the students in an AP
Statistics class are planning a random survey of 100
students to estimate the proportion who would rather drop
lacrosse rather than band during this time of severe budget
cuts. Their teacher suggests instead to survey 200 students
in order to
(A) reduce bias.
(B) reduce variability.
(C) increase bias.
(D) increase variability.
(E) make possible stratification between lacrosse and band.
7. Changing from a 95% confidence interval estimate for a
population proportion to a 99% confidence interval
estimate, with all other things being equal,
(A) increases the interval size by 4%.
(B) decreases the interval size by 4%.
(C) increases the interval size by 31%.
(D) decreases the interval size by 31%.
(E) This question cannot be answered without knowing the
sample size.
4. The ages of people who died last year in the United
States is skewed left. What happens to the sampling
distribution of sample means as the sample size goes from
𝑛 = 50 to 𝑛 = 200?
(A) The mean gets closer to the population mean, the
standard deviation stays the same, and the shape becomes
more skewed left.
8. A confidence interval estimate is determined from the
GPAs of a simple random sample of n students. All other
things being equal, which of the following will result in a
smaller margin of error?
(A) A smaller confidence level
(B) A larger sample standard deviation
(C) A smaller sample size
(D) A larger population size
(E) A smaller sample mean
9. A survey was conducted to determine the percentage of
high school students who planned to go to college. The
results were stated as 82% with a margin of error of ±5%.
What is meant by ±5%?
(A) Five percent of the population were not surveyed.
(B) In the sample, the percentage of students who plan to
go to college was between 77% and 87%.
(C) The percentage of the entire population of students
who plan to go to college is between 77% and 87%.
(D) It is unlikely that the given sample proportion result
would be obtained unless the true percentage was between
77% and 87%.
(E) Between 77% and 87% of the population were
surveyed.
10. Most recent tests and calculations estimate at the 95%
confidence level that the maternal ancestor to all living
humans called mitochondrial Eve lived 273,000 ± 177,000
years ago. What is meant by "95% confidence" in this
context?
(A) A confidence interval of the true age of mitochondrial
Eve has been calculated using z-scores of ±1.96.
(B) A confidence interval of the true age of mitochondrial
Eve has been calculated using t-scores consistent with df =
n - 1 and tail probabilities of ±.025.
(C) There is a .95 probability that mitochondrial Eve lived
between 96,000 and 450,000 years ago.
(D) If 20 random samples of data are obtained by this
method, and a 95% confidence interval is calculated from
each, then the true age of mitochondrial Eve will be in 19
of these intervals.
(E) 95% of all random samples of data obtained by this
method will yield intervals that capture the true age of
mitochondrial Eve.
11. In a recent Zogby International survey, 11% of 10,000
Americans under 50 said they would be willing to implant
a device in their brain to be connected to the Internet if it
could be done safely. What is the margin of error at the
99% confidence level?
for integration. What size voter sample should be obtained
to determine with 90% confidence the support level to
within 4%?
(A) 21
(B) 25
(C) 423
(D) 600
(E) 1691
13. In a simple random sample of 300 elderly men, 65%
were married, while in an independent simple random
sample of 400 elderly women, 48% were married.
Determine a 99% confidence interval estimate for the
difference between the proportions of elderly men and
women who are married.
14. Two confidence interval estimates from the same
sample are (16.4, 29.8) and (14.3, 31.9). What is the
sample mean, and if one estimate is at the 95% level while
the other is at the 99% level, which is which?
(A) 𝑥̅ =23.1; (16.4, 29.8) is the 95% level.
(B) 𝑥̅ =23.1; (16.4, 29.8) is the 99% level.
(C) It is impossible to completely answer this question
without knowing the sample size.
(D) It is impossible to completely answer this question
without knowing the sample standard deviation.
(E) It is impossible to completely answer this question
without knowing both the sample size and standard
deviation.
15. Nine subjects, 87 to 96 years old, were given 8 weeks
of progressive resistance weight training (Journal of the
American Medical Association, June 13, 1990, page 3032).
Strength before and after training for each individual was
measured as maximum weight (in kilograms) lifted by left
knee extension:
Find a 95% confidence interval estimate for the strength
gain.
(A) 11.61 ± 3.03
(B) 11.61 ± 3.69
(C) 11.61 ± 3.76
(D) 19.11 ± 1.25
(E) 19.11 ± 3.69
12. A politician wants to know what percentage of the
voters support her position on the issue of forced busing
16. You plan to perform a hypothesis test with a level of
significance of 𝛼 = .05. What is the effect on the
probability of committing a Type I error if the sample size
is increased?
(A) The probability of committing a Type I error
decreases.
(B) The probability of committing a Type I error is
unchanged.
(C) The probability of committing a Type I error increases.
(D) The effect cannot be determined without knowing the
relevant standard deviation.
(E) The effect cannot be determined without knowing if a
Type II error is committed.
17. A research dermatologist believes that cancers of the
head and neck will occur most often of the left side, the
side next to a window when a person is driving. In a
review of 565 cases of head/neck cancers, 305 occurred on
the left side. What is the resulting P-value?
18. Suppose you do five independent tests of the form
𝐻0 : 𝜇 = 38 versus 𝐻𝑎 : 𝜇 > 38, each at the 𝛼 = .01
significance level. What is the probability of committing a
Type I error and incorrectly rejecting a true null hypothesis
with at least one of the five tests?
(A) .01
(B) .049
(C) .05
(D) .226
(E) .951
19. Suppose 𝐻0 : 𝑝 = 4, and the power of the test for the
alternative hypothesis 𝑝 = .35 is . 75. Which of the
following is a valid conclusion?
(A) The probability of committing a Type I error is .05.
(B) The probability of committing a Type II error is .65.
(C) If the alternative 𝑝 = .35 is true, the probability of
failing to reject 𝐻0 is .25.
(D) If the null hypothesis is true, the probability of
rejecting it is .25.
(E) If the null hypothesis is false, the probability of failing
to reject it is .65.
20. A pharmaceutical company claims that 8% or fewer of
the patients taking their new statin drug will have a heart
attack in a 5-year period. In a government-sponsored study
of 2300 patients taking the new drug, 198 have heart
attacks in a 5-year period. Is this strong evidence against
the company claim?
(A) Yes, because the P-value is .005657.
(B) Yes, because the P-value is .086087.
(C) No, because the P-value is only .005657.
(D) No, because the P-value is only .086087.
(E) No, because the P-value is over .10.