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AP Statistic
#22-AP Review – One Sample Inference Mixed with Answers
1) Which of the following is not true about constructing confidence
intervals?
a) The value of the standard error is a function of the sample
statistic.
b) The center of the confidence interval is the population
parameter.
c) One of the values that affect the width of a confidence interval
is the sample size.
d) If the value of the population parameter is known, it is
irrelevant to calculate a confidence interval for it.
e) The value of the confidence level will affect the width of a
confidence interval.
2) When determining sample size for a study dealing with a
proportion, it is most conservative to use 0.5 as an estimate of the
sample proportion. Which of the following is the reason for this fact?
a) The study will focus only on two responses: success and
failure.
b) 0.5 is the probability of flipping a coin. Since the survey deals
only with a yes/no question, this probability is appropriate.
c) 0.5 will produce the greatest standard error. Therefore, the
sample size using this value will guarantee that the margin of
error for the study will be maximized.
d) This is a binomial probability situation in which n is a sample
size, p = 0.5, and r is the number of positive responses.
e) None of these explains the use of 0.5 for the calculation of the
most conservative sample size.
3) A large company wants to find out what kinds of transportation its
employees use to get to work. It conducts a random survey of 55
employees, and 25 say they ride a bus. Construct a 95% confidence
interval for the proportion of employees who ride the bus to work.
a) (.32, .59)
d) (.41, .68)
b) (.34, .56)
e) (.43, .66)
c) (.28, .63)
4) Which of the following are true of the margin of error for a single
population proportion?
I. Multiply the margin of error by z* to get the standard error.
II. The margin of error is a calculation that describes the error
introduced into a study when the sample isn’t truly random.
III. The margin of error describes a possible random sampling
error that occurs within truly random samples.
a) I only
d) I and II only
b) II only
e) I and III only
c) III only
5) You want to estimate the proportion of people who experience
computer crashes when they access a website. Calculate the minimum
sample size you would need to ensure a 4% margin of error for a 95%
confidence interval.
a) 505
d) 1074
b) 601
e) 2401
c) 673
6) Which of the following do we not need to assume is true in order to
carry out a hypothesis test about a single proportion?
a) np > 10
b) SRS
c) n(1 – p) > 10
d) pˆ = .5
e) The population of interest is at least 10 times larger than the
sample.
7) You are interested in determining whether there’s a difference in
people’s preferences for orange or pink food. To see if there is a
difference, you make a large batch of vanilla pudding and dye half
orange and the other half pink. You record the proportion of people
who prefer pink. What will your hypotheses be?
a) H0: p = 0.5; Ha: p > 0.5
b) H0: p̂ = 0.5; Ha: p̂ ≠ 0.5
c) H0: p = 0.5; Ha: p < 0.5
d) H0: p = 0.5; Ha: p ≠ 0.5
e) H0: p̂ = 0.5; Ha: p̂ < 0.5
8) The choice of hypothesis test
a) should be made after all possible tests are performed using
technology.
b) is critical only in the case of medical experiments.
c) depends only on the parameter of interest.
d) depends on the parameter of interest, the sampling situation,
and the type of variable involved.
e) is left to the tester whenever n is greater than or equal to 30.
9) Which of the following is not true?
a) A way to reduce Type II errors is to increase sample size.
b) If sample size remains constant, then reducing α will increase
the value of β.
c) α depends on the null hypothesis; β depends on both the null
hypothesis and the value of an alternative mean.
d) For the hypothesis test of a parameter, α must equal β.
e) All of these are correct.
10) In a hypothesis test, the decision between a one-sided and a twosided alternative hypothesis is based on
a) which one gives you a significant result.
b) the alternative hypothesis appropriate for the context of the
problem.
c) how accurate you wish the results of the test.
d) the level of significance of the test.
e) the statement of the null hypothesis.
12) Which of the following will reduce the width of a confidence
interval?
a) Increase the confidence level
b) Decrease the sample size
c) Add 0.5 to the sample proportion
d) Replace the sample proportion with 0.5
e) None of these will guarantee a decrease in the width of the
confidence interval.
13) Which of the following statements is correct?
a) A sample statistic is significant if its population parameter is
significant.
b) A sample statistic is significant if it is very unlikely that such a
statistic could come from a sample of this size drawn from the
population.
c) A sample statistic is significant if it can be established that it
results from bias in the data-gathering process.
d) A sample statistic that is significant is always important.
e) All of these are correct.
14) Given α = 0.05, which of the following is true?
a) β = 0.95
b) The power of the test is 0.95.
c) α = P(rejecting H0 when H0 is true)
d) α = P(rejecting H0 when H0 is false)
e) The value of α is independent of the value of β.
15) In the picture below, the value of α is in which region?
11) A TV news magazine states that the results of their study of the
average number of complaints per week about garbage pick-up in the
city had a margin or error of + 2.1% at the 95% confidence level,
based on their examination of data from a random sample of a total of
30 weeks over the past 3 years. For this statement to be true, what was
the appropriate population standard deviation that the organization
must have used to compute the margin of error?
a) 4.31
d) 0.20
b) 5.87
e) 0.75
c) 8.65
1
a)
b)
c)
d)
e)
1
2
3
4
α
a
2 3
0
4
16) An SRS of size n is taken from a large population whose distribution of income
is extremely right-skewed and the mean income is calculated. Which of the
following statements is false?
a) When n > 30, the sampling distribution of x is approximately normal.
b) When n increases, the sample standard deviation decreases (s).

c) The standard deviation of the sampling distribution of x is
.
n
d) The standard error is the standard deviation of the sample (s).
e) When n increases, the standard deviation of the sampling distribution of x
decreases.
17) John scored 113 on a particular standardized achievement test. The scores on the
test are distributed with a mean of 100 and a standard deviation of 10. His cousin,
Brandon, took a different standardized test and scored 263. The scores on Brandon’s
test have a mean of 250 and a standard deviation of 25. Which student did better on
his particular test?
a) John did better on his test.
b) Brandon did better on his test.
c) They both performed equally well on their respective tests.
d) It is impossible to tell since they did not take the same test.
e) It is impossible to tell since the number of students taking the test is unknown.
18) The power of a significance test for a particular value of the parameter is
computed to be 0.93. Which statement below is true?
a) The probability of committing a Type I error is 0.07.
b) The probability of committing a Type I error is 0.93.
c) The probability of committing a Type II error is 0.07.
d) The probability of committing a Type II error is 0.93.
e) The probability of committing a Type II error is the same as the alpha level.
19) A baseball coach wants to compare the number of hits be two groups of batters
each using a different type of bat. Which type of graphical display would not be
appropriate?
a) parallel boxplots
d) histograms drawn on the same scale
b) dotplots drawn on the same scale
e) scatterplot
c) back-to-back stemplots
20) Who makes more mistakes on their income tax forms: accountants or tax-payers
who prepare the forms themselves? A random sample of income tax forms that were
prepared by accountants was drawn from IRS records. An equal number of forms
that were self-prepared by tax-payers were also randomly drawn. The average
number of errors per form was compared to determine if one group tends to make
more mistakes than the other. What type of study is this?
a) census
c) voluntary response
e) matched-pairs
b) experiment
d) observational
21) A dance club holds a raffle at the end of each dance. Five selected dancers will
draw one numbered tag from a hat without replacement. There are 50 tags in the hat
numbered 1 to 50. Drawing a tag from 1 – 5 wins $20, tags 6 – 25 wins $10 and tags
26-50 wins $5. In order to determine the average amount of money paid out, a
simulation will be conducted using a random number table. Which of the following
assignments of random numbers to tag values is most appropriate for this
simulation?
a) Using single-digit numbers, assign 0 to represent a $20 prize, 1-4 represent a $10
prize, and 5-9 represent a $5 prize.
b) Using single-digit numbers, assign 0 to represent a $20 prize, 1 represents a $10
prize, 2 represents a $5 prize, and ignore digits 3-9.
c) Using double-digit numbers, assign 20 to represent a $20 prize, 10 represents a
$10 prize, 05 represents a $5 prize, and ignore numbers 0-04, 06-09, 11-19, 21-99.
d) Using double-digit numbers, assign 01-05 to represent a $20 prize, 06-25
represent a $10 prize, 26-50 represent a $5 prize, and ignore numbers 51-99 and 00.
e) Using double-digit numbers, assign 01-10 to represent a $20 prize, 11-40
represent a $10 prize, and 41-99 & 00 represent a $5 prize.
22) A hypothesis test is conducted with respect to the mean weight (in ounces) of
potato chip bags form a certain manufacturer. The hypotheses are: H 0: μ = 0.8 and
Ha: μ ≠ 0.8. Which confidence level would support the conclusion that there is
insufficient evidence to reject H0 when α
a) 97%
b) 94%
c) 95%
d) 98.5%
e) 90%
23) The student council wants to survey students at the school to see what brands of
soda pop they want in the school machines. They randomly sampled 30 freshmen,
30 sophomores, 30 juniors, and 30 seniors. The sampling method they used is a
a) simple random sample
d) systematic random sample
b) stratified random sample
e) convenience sample
c) cluster sample
Answers:
1–B, 2–C, 3-A, 4-C, 5-B, 6-D, 7-D, 8-D, 9-D, 10-B, 11-B, 12-E,
13-B, 14-C, 15-C, 16-B, 17-A, 18-C, 19-E, 20-D, 21-D, 22-A
23-B, 24-C, 25-D, 26-B, 27-D, 28-B, 29-D, 30-C, 31-B
24) Which of the following is a legitimate probability distribution?
a)
X
3
4
5
6
P(X)
0.1
0.1
0.1
0.1
b)
X
P(X)
0
0.2
1
0.1
2
0.1
3
0.2
4
0.2
c)
X
P(X)
-5
0.6
0
0.1
5
0.2
10
0.1
15
0
d)
X
P(X)
1
0.3
3
0.2
5
0.2
7
0.4
e)
X
P(X)
1
0.05
1.5
0.08
2
0.08
2.5
0.20
3
0.30
5
0.3
3.5
0.10
4
0.21
4.5
-0.01
25) A tire manufacturer is testing a new tread design for its light-truck tires. The
previous design had a mean tread life of 47,500 miles. Tires with the new design are
manufactured and tested on a variety of light trucks. Which of the following is the
correct pair of hypotheses to test the assertion that the new tread design has a longer
life than the old design?
a) H0: μ < 47,500, Ha: μ = 47,500
d) H0: μ = 47,500, Ha: μ > 47,500
b) H0: μ = 47,500, Ha: μ ≠ 47,500
e) H0: μ > 47,500, Ha: μ < 47,500
c) H0: μ = 47,500, Ha: μ < 47,500
26) A distribution of scores has a mean of 60 and a standard deviation of 18. If each
score is doubled, and then 5 is subtracted from the result, what will be the mean and
standard deviation of the new scores?
a) μ = 115, σ = 31
c) μ = 120, σ = 6
e) μ = 120, σ = 36
b) μ = 115, σ = 36
d) μ = 120, σ = 31
27) A doll-making company has been able to streamline their production process by
having three jobs: assembling the doll, putting clothing on the doll, and putting the
doll in the box. The table illustrates the mean time (in seconds) and standard
deviation for each task. The distributions of times for each step are approximately
normal and independent. What are the mean and standard deviation of the total time
(in seconds) to complete all three tasks?
a) μ = 60.6 & σ = 3.17
b) μ = 60.6 & σ = 5.05
Mean
Standard deviation
c) μ = 66 & σ = 0.88
Assembly
36
2.5
d) μ = 66 & σ = 3.17
Clothing
22
1.8
e) μ = 66 & σ = 5.05
Boxing
8
0.75
28) Some AP Statistics students were interested in finding out if there was a
relationship between the number of hours of study for a chapter test and the score on
that test. On the basis of the number of hours their classmates student for the chapter
3 test and scores on the test (out of 100%), the LSRL calculated
was yˆ  72.53  5.88x , where x is the number of hours studied and yˆ is the
predicted score on the test. Which statement correctly interprets the meaning of the
slope of this regression line?
a) For each additional hour studied, the predicted score on the test increase by
approximately 73%.
b) For each additional hour studied, the predicted score on the test increase by
approximately 6%.
c) For each additional percent of increase on the test, the predicted score on the test
increase by approximately 73%.
d) For each additional percent of increase on the test, the predicted score on the test
increase by approximately 6%.
e) We cannot use this regression equation, since cause-effect has not been proven.
29) A certain variety of table grapes has fruit diameters that are distributed normally
with mea 13 mm and standard deviation 2 mm. Approximately what proportion of
grapes have diameters between 12mm and 16 mm?
a) 0.134
b) 0.378
c) 0.500
d) 0.625
e) 0.683
30) The Sunday edition of the newspaper has 585,320 readers. Sixty-three percent of
the readers are men. It is known that about 12% of the women and 23% of the mean
that read this newspaper will read the book review section. If a random sample of
200 readers is taken, what is the expected number of people that will read the book
review section?
a) 23
b) 24
c) 38
d) 46
e) 70
31) A major automobile manufacturer is trying to improve its customer service at its
dealerships across the United States. A survey of 200 customers in Arizona who
recently purchased a vehicle from this manufacturer was asked if they were satisfied
with the customer service at the dealership. Is it reasonable to generalize the
conclusion to the population of all customers in the United States that purchased
from this manufacturer?
a) No, because 200 is not a large enough sample.
b) No, because customers were only sampled in one state.
c) No, because only one sample was taken.
d) Yes, because the sample size is more than 30.
e) Yes, because the population of all new vehicle owners by this manufacturer is
more than 2000.