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AP Statistics Question Bank
• White: Practice AP Statistics test (complied
from collegeboard.com)
• Blue: 1997 AP Statistics test
• Orange: Sample questions from AP Course
Description
Unit 1: Displaying Univariate Data
• 3a. Organize data using graphs that are appropriate to
the data set, including frequency distributions, stacked
line and bar graphs, stem-and-leaf plots, scatter plot,
frequency polygon, and histograms. (DOK 2)
• 4a. Make inferences and predictions from charts,
tables, and graphs that summarize data. (DOK 3)
• 3b. Determine and justify the graph type that best
represents a given set of data. (DOK 2)
• 3c. Create graphs with scales that fairly display the
data. (DOK 2)
• Types of data (categorical/quantitative)
• Pie charts
22) The back-to-back stem-and-leaf plot below gives the percentage of students who
dropped out of school at each of the 49 schools in a large metropolitan school district.
1989-1990
1992-1993
0 4
4444444333311110 1 00001111222334444
9997766664 1 555666677778
4222100 2 13
88876 2
2 3 0112
766 3 5
4
Which of the following statements is NOT justified by these data?
A. The drop-out decreased in each of the 49 high schools between the 1989-1990 and 19921993
B. For the school years shown, most students in the 49 high schools did not drop out of high
school.
C. In general, drop-out rates decreased between the 1989-1009 and 1992-1993 school years.
D. The median drop-out rate of the 49 high schools decreased between the 1989-1990 and
1992-1993 school years.
E. The spread between the schools with the lowest drop-out rates and those with the
highest drop-out rates did not change much between the 1989-1990 and 1992-1993 school
years.
26) A fair coin is flipped 10 times and the number of heads is counted. The
procedure of 10 coin flips is repeated 100 times and the results are placed
in a frequency table. Which of the frequency tables below is most likely to
contain the results from these 100 trials?
Head
Freq
Head
Freq
Head
Freq
Head
Freq
Head
Freq
0
19
0
9
0
0
0
7
0
0
1
12
1
9
1
0
1
10
1
0
2
9
2
9
2
6
2
6
2
0
3
6
3
9
3
9
3
11
3
2
4
2
4
9
4
22
4
8
4
24
5
1
5
10
5
24
5
10
5
51
6
3
6
9
6
18
6
9
6
22
7
5
7
9
7
12
7
12
7
1
8
8
8
9
8
7
8
7
8
0
9
14
9
9
9
2
9
11
9
0
10
21
10
9
10
0
10
9
10
0
Unit 2: Describing Univariate Data
• 2b. Calculate mean, median, mode, standard deviation,
z-scores, t-scores, quartiles, and ranges, and explain
their applications. (DOK 2)
• 1a. Describe the comparison of center and spread
within groups and between or across group variation.
(DOK 2)
• 4b. Determine the most appropriate measure to
describe a data set, including mean, median, mode,
standard deviation, and variance. (DOK 2)
• Box plots
• Empirical rule
• Percentiles
8. Consider a data set of positive values, at least two of
which are not equal. Which of the following sample
statistics will be changed when each value in this data
set is multiplied by a constant whose absolute value is
greater than 1?
I. The mean
II. The median
III. The standard deviation
A.
B.
C.
D.
E.
I only
II only
III only
I and II only
I, II, and III
Variable
Score
N
50
Mean
1045.7
Median
1024.7
TrMean
1041.9
Variable
Score
Minimum
628.9
Maximum
1577.1
Q1
877.7
Q3
1219.5
StDev
221.9
SE Mean
31.4
5. Some descriptive statistics for a set of test scores are shown
above. For this test, a certain student has a standardized
score of z = -1.2. What score did this student receive on the
test?
A.
B.
C.
D.
E.
266.28
779.42
1008.02
1083.38
1311.98
25) At a college the scores on the chemistry final exam are
approximately normally distributed, with a mean of 75 and a
standard deviation of 12. The scores on the calculus final are also
approximately normally distributed, with a mean of 80 and a
standard deviation of 8. A student scores 81 on the chemistry
final and 84 on the calculus final. Relative to the students in each
respective class, in which subject did this student do better?
A. The student did better in chemistry.
B. The student did better in calculus.
C. The student did equally well in each course.
D. There is no basis for comparison, since the subjects are
different from each other and are in different departments.
E. There is not enough information for comparison, because the
number of students in each class is not known.
12) The heights of adult women are approximately
normally distributed about a mean of 65 inches
with a standard deviation of 2 inches. If Rachael
is at the 99th percentile in height for adult
women, then her height, in inches, is closest to
A.
B.
C.
D.
E.
60
62
68
70
74
21. Below, the cumulative frequency plot shows
height (in inches) of college basketball players.
What is the interquartile range?
(A) 3 inches
(B) 6 inches
(C) 25 inches
(D) 50 inches
(E) None of the above
10)The boxplots above summarize two data sets, A
and B. Which of the following must be true?
I. Set A contains more data than Set B.
II. The box of Set A contains more data than
the box of Set B.
III. The data in Set A have a large range than
the data in Set B.
A.
B.
C.
D.
E.
I only
III only
I and III only
II and III only
I, II, and III
**bell curve, 30-40-50-60-70**
15)Which of the following is the best estimate of
the standard deviation of the distribution
shown in the figure above?
A.
B.
C.
D.
E.
5
10
30
50
60
25. The back-to-back stemplot on the right shows the number of books read in a year
by a random sample of college and high school students. Which of the following
statements are true?
I. One college student read seven books.
II. The college median is equal to the high school median.
III. The mean is greater than the median in both groups.
(A) I only
(B) II only
(C) I and III only
(D) II and III only
(E) I, II, and III
College
7
366
1234
6889
28
0
1
2
3
4
5
6
3 7
High school
0035
12446
189
01
21) A company wanted to determine the health care costs of
its employees. A sample of 25 employees were
interviewed and their medical expenses for the previous
year were determined. Later the company discovered
that the highest medical expense in the sample was
mistakenly recorded as 10 times the actual amount.
However, after correcting the error, the corrected amount
was still greater than or equal to any other medical
expenses in the sample. Which of the following sample
statistics must have remained the same after the
correction was made?
A.
B.
C.
D.
E.
Mean
Median
Mode
Range
Variance
17) Gina’s doctor told her that the standardized score (zscore) for her systolic blood pressure, as compared to the
blood pressure of other women her age, is 1.50. Which of
the following is the best interpretation of this
standardized score?
A. Gina’s systolic blood pressure is 150.
B. Gina’s systolic blood pressure is 1.50 standard
deviation above the average systolic blood pressure of
women her age.
C. Gina’s systolic blood pressure is 1.50 above the average
systolic blood pressure of women her age.
D. Gina’s systolic blood pressure is 1.50 times the average
systolic blood pressure for women her age.
E. Only 1.5% of women Gina’s age have a higher systolic
blood pressure than she does.
34. Molly earned a score of 940 on a national
achievement test. The mean test score was
850 with a standard deviation of 100. What
proportion of students had a higher score
than Molly? (Assume that test scores are
normally distributed.)
(A) 0.10
(B) 0.18
(C) 0.50
(D) 0.82
(E) 0.90
5. A sample consists of four observations: {1, 3,
5, 7}. What is the standard deviation?
(A) 2
(B) 2.58
(C) 6
(D) 6.67
(E) None of the above
9. A national achievement test is administered
annually to 3rd graders. The test has a mean
score of 100 and a standard deviation of 15. If
Jane's z-score is 1.20, what was her score on
the test?
(A) 82
(B) 88
(C) 100
(D) 112
(E) 118
13. The stemplot below shows the number of hot dogs eaten by contestants in a
recent hot dog eating contest.
80
70
60
50
40
30
20
10
1
47
226
025799
579
79
1
Which of the following statements are true?
I. The range is 70.
II. The median is 46.
III. The mean is 47.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
22. Suppose X and Y are independent random
variables. The variance of X is equal to 16; and
the variance of Y is equal to 9. Let Z = X - Y.
What is the standard deviation of Z?
(A) 2.65
(B) 5.00
(C) 7.00
(D) 25.0
(E) It is not possible to answer this question,
based on the information given.
17. Consider the boxplot below.
Which of the following statements are true?
I. The distribution is skewed right.
II. The interquartile range is about 8.
III. The median is about 10.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Unit 3: Describing Bivariate Data
• 3a. Organize data using scatter plots. (DOK 2)
• 2a. Analyze and describe outliers and shape of the data including
linearity and correlation across graphs and data sets. (DOK 2)
• 2d. Use algebraic concepts and methods to determine
mathematical models of best fit. (DOK 2)
• 4c. Use curve-fitting to make predictions from collected data. (DOK
2)
• 4d. Explain and defend regression models using correlation
coefficients and residuals. (DOK 2)
• Explanatory v. response variables
• Causation, lurking variables
• Extrapolation
• Transforming data
14.Consider n pairs of numbers (x1, y1), (x2, y2), … ,
and (xn, yn). The mean and standard deviation
of the x-values are meanx = 5 and sx = 4,
respectively. The mean and standard deviation
of the y-values are meany = 10 and sy = 10,
respectively. Of the following, which could be
the least squares regression line?
A.
B.
C.
D.
E.
y = -5.0 + 3.0x
y = 3.0x
y = 5.0 + 2.5x
y = 8.5 + 0.3x
y = 10.0 + 0.4x
12. Exercise physiologists are investigating the relationship between lean body mass
(in kilograms) and the resting metabolic rate (in calories per day) in sedetary
males.
Predictor
Constant
Mass
Coef
264.0
22.563
StDev
276.9
6,360
S = 144.9
R-SQ = 55.7%
T
0.95
3.55
P
0.363
0.005
R-Sq(adj) = 51.3%
Based on the computer output above, which of the following is the best
interpretation of the value of the slope of the regression line?
A.
B.
C.
D.
E.
For each individual kilogram of lean body mass, the resting metabolic rate
increases on average by 22.563 calories per day.
For each individual kilogram of lean body mass, the resting metabolic rate
increases on average 264.0 calories per day.
For each individual kilogram of lean body mass, the resting metabolic rate
increases on average by 144.9 calories per day.
For each individual calorie per day for the resting metabolic rate, the lean body
mass increases on average by 22.563 kilograms.
For each additional calorie per day for the resting metabolic rate, the lean body
mass increases on average by 264.0 kilograms.
**scatterplot***
1. In the scatterplot of y versus x shown above,
the least squares regression line is
superimposed on the plot. Which of the
following points has the largest residual?
A.
B.
C.
D.
E.
A
B
C
D
E
Job
No job
Total
Juniors
13
5
18
Seniors
13
26
39
Total
26
31
57
14) A survey of 57 students was conducted to determine whether or not they held jobs
outside of school. The two-way table above shows the numbers of students by
employment status (job, no job) and class (juniors, seniors). Which of the following
best describes the relationship between employment status and class?
A. There appears to be no association, since the same number of juniors and
seniors have jobs.
B. There appears to be no association, since close to half of the students have jobs.
C. There appears to be an association, since there are more seniors than juniors in
the survey.
D. There appears to be an association, since the proportion of juniors having jobs is
much larger than the proportion of seniors having jobs.
E. A measure of association cannot be determined from these data.
***graph***
13) The equation of the least squares regression line for
the points on the scatter plot above is y = 1.3 + 0.73x.
What is the residual for the point (4, 7)?
A.
B.
C.
D.
E.
2.78
3.00
4.00
4.22
7.00
28) There is a linear relationship between the number of
chirps made by the striped ground cricket and the air
temperature. A least squares fit of some data collected by
a biologist gives the model
y = 25.2 + 3.3x
9 < x < 25
where x is the number of chirps per minute and y is the
estimated temperature in degrees Fahrenheit. What is
the estimated increase in temperature that corresponds
to an increase of 5 chirps per minute?
A.
B.
C.
D.
E.
3.3°F
16.5°F
25.2°F
28.5°F
41.7°F
37. In the context of regression analysis, which of the
following statements are true?
I. A linear transformation increases the linear
relationship between variables.
II. A logarithmic model is the most effective
transformation method.
III. A residual plot reveals departures from linearity.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
33. In the context of regression analysis, which of the
following statements are true?
I. When the sum of the residuals is greater than zero,
the model is nonlinear.
II. Outliers reduce the coefficient of determination.
III. Influential points reduce the correlation coefficient.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
29. A national consumer magazine reported the following
correlations.
The correlation between car weight and car reliability is -0.30.
The correlation between car weight and annual maintenance cost is
0.20.
Which of the following statements are true?
I. Heavier cars tend to be less reliable.
II. Heavier cars tend to cost more to maintain.
III. Car weight is related more strongly to reliability than to
maintenance cost.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
Unit 4: Sampling, Experiments
• 5c. Analyze sources of bias and sampling error(s)
in studies. (DOK 3)
• 5d. Compare and contrast sampling methods,
including simple random sampling, stratified
random sampling, and cluster sampling with
regard to benefits and trade-offs. (DOK 2)
• 5b. Explain the generalizability of results and
types of conclusions that can be drawn from
observational studies, empirical experiments, and
surveys. (DOK 2)
16. George and Michelle each claimed to have the better recipe for
chocolate chip cookies. They decided to conduct a study to determine
whose cookies were really better. They each bakes a batch of cookies
using their own recipe. George asked a random sample of his friends to
taste his cookies and to complete a questionnaire on their quality.
Michelle asked a random sample of her friends to complete the same
questionnaire for her cookies. They then compared the results. Which
of the following statements about this study is false?
A.
B.
C.
D.
E.
Because George and Michelle have a different population of friends,
their sampling procedure makes it difficult to compare the recipes.
Because George and Michelle each used only their own respective
recipes, their cooking ability is confounded with the recipe quality.
Because George and Michelle each used only the ovens in their houses,
the recipe quality is confounded with the characteristics of the oven.
Because George and Michelle used the same questionnaire, their results
will generalize to the combined population of their friends.
Because George and Michelle each baked one batch, there is no
replication of the cookie recipes.
9. Each person in a simple random sample of 2,000 received
a survey, and 317 people returned their survey. How
could nonresponse cause the results of the survey to be
biased?
A. Those who did not respond reduced the sample size, and
small samples have more bias then large samples.
B. Those who did not respond caused a violation of the
assumption of independence.
C. Those who did not respond were indistinguishable from
those who did not receive the survey.
D. Those who did not respond represent a stratum, changing
the simple random sample into a stratified random
sample.
E. Those who did not respond may differ in some important
way from those who did respond.
2. Under which of the following conditions is it preferable to
use stratified random sampling rather than simple random
sampling?
A. The population can be divided into a large number of
strata so that each stratum only contains a few
individuals.
B. The population can be divided into a small number of
strata so that each stratum contains a large number of
individuals.
C. The population can be divided into strata so that the
individuals in each stratum are as much alike as possible.
D. The population can be divided into strata of equal size so
that each individual in the population still has the same
chance of being selected.
27) The student government at a high school wants to conduct a
survey of student opinion. It wants to begin with a simple random
sample of 60 students. Which of the following survey methods
will produce a simple random sample?
A. Survey the first 60 students to arrive at school in the morning.
B. Survey every 10th student entering the school library until 60
students are surveyed.
C. Use random numbers to choose 15 each of first-year, secondyear, third-year, and fourth-year students.
D. Number the cafeteria seats. Use a table of random numbers to
choose seats and interview the students until 60 have been
interviewed.
E. Number the students in the official school roster. Use a table
of random numbers to choose 60 students from this roster for the
survey.
18) The Physician’s Health Study, a large medical experiment involving 22,000
make physicians, attempted to determine whether aspirin could help
prevent heart attacks. In this study, one group of about 11,000 physicians
took an aspirin every other day, while a control group took a placebo.
After several years, it was determined that the physicians in the group that
took aspirin had significantly fewer heart attacks than the physicians in the
control group. Which of the following statements explains why it would
not be appropriate to say that everyone should take an aspirin every other
day?
I. The study included only physicians, and different results may occur
in individuals in other occupations.
II. The study included only males and there may be different results
for females.
III. Although taking aspirin may be helpful in preventing heart
attacks, it may be harmful to some other aspects of health.
A.
B.
C.
D.
E.
I only
II only
III only
II and III only
I, II, and III
9) To check the effect of cold temperature on the elasticity of
two brands of rubber bands, one box of Brand A and one
box of Brand B rubber bands are tested. Ten bands from
the Brand A box are placed in a freezer for two hours and
ten bands from the Brand B box are kept at room
temperature. The amount of stretch before breakage is
measured on each rubber band, and the mean for the
cold bands is compared to the mean for the others. Is this
a good experimental design?
A. No, because the means are not proper statistics for
comparison
B. No, because more than two brands should be used.
C. No, because more temperatures should be used.
D. No, because temperature is confounded with brand.
E. Yes
8) Which of the following can be used to show a
cause-and-effect relationship between two
variables?
A.
B.
C.
D.
E.
A census
A controlled experiment
An observational study
A sample survey
A cross-sectional survey
1. Which of the following statements are true? (Check
one)
I. Categorical variables are the same as qualitative
variables.
II. Categorical variables are the same as quantitative
variables.
III. Quantitative variables can be continuous variables.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
3. An auto analyst is conducting a satisfaction survey, sampling
from a list of 10,000 new car buyers. The list includes 2,500
Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and
2,500 Toyota buyers. The analyst selects a sample of 400
car buyers, by randomly sampling 100 buyers of each
brand.
Is this an example of a simple random sample?
(A) Yes, because each buyer in the sample was randomly
sampled.
(B) Yes, because each buyer in the sample had an equal
chance of being sampled.
(C) Yes, because car buyers of every brand were equally
represented in the sample.
(D) No, because every possible 400-buyer sample did not
have an equal chance of being chosen.
(E) No, because the population consisted of purchasers of
four different brands of car.
11. Which of the following statements are true?
I. A sample survey is an example of an
experimental study.
II. An observational study requires fewer
resources than an experiment.
III. The best method for investigating causal
relationships is an observational study.
(A) I only
(B) II only
(C) III only
(D) All of the above.
(E) None of the above.
19. Which of the following statements are true?
I. Random sampling is a good way to reduce response
bias.
II. To guard against bias from undercoverage, use a
convenience sample.
III. Increasing the sample size tends to reduce survey
bias.
IV. To guard against nonresponse bias, use a mail-in
survey.
(A) I only
(B) II only
(C) III only
(D) IV only
(E) None of the above.
27.With respect to experimental design, which of
the following statements are true?
I. Blinding controls for the effects of confounding.
II. Randomization controls for effects of lurking
variables.
III. Each experimental factor has one treatment
level.
(A) I only
(B) II only
(C) III only
(D) All of the above.
(E) None of the above.
35. Which of the following statements are true?
I. A completely randomized design offers no
control for lurking variables.
II. A randomized block design controls for the
placebo effect.
III. In a matched pairs design, subjects within
each pair receive the same treatment.
(A) I only
(B) II only
(C) III only
(D) All of the above.
(E) None of the above.
Unit 5: Probability
•
•
•
•
•
•
•
•
•
•
•
1b. Interpret and apply the concept of the Law of Large Numbers. (DOK 2)
1d. Construct and interpret sample spaces, events, and tree diagrams. (DOK 2)
1e. Identify types of events, including mutually exclusive, independent, and
complements. (DOK 1)
1g. Create simulations and experiments that correlate to theoretical probability.
(DOK 2)
1i. Apply the concept of a random variable to generate and interpret probability
distributions. (DOK 2)
1f. Calculate geometric probability using two-dimensional models, and explain the
processes used. (DOK 2)
Multiplication, Addition Rules
Discrete v. continuous variables
Expected value, standard deviation of a random variable
Bernoulli trials
Binomial, geometric, and normal models
10.In a certain game, a fair die is rolled and a player
gains 20 points if the die shows a “6.” If the die
does not show a “6,” the player loses 3 points. If
the die were to be rolled 100 times, what would
be the expected total gain or loss for the player?
A.
B.
C.
D.
E.
A gain of about 1,700 points
A gain of about 583 points
A gain of about 83 points
A gain of about 250 points
A loss of about 300 points
7. A summer resort rents rowboats to customers but
does not allow more than four people to a boat. Each
boat is designed to hold no more than 800 pounds.
Suppose the distribution of adult males who rent
boats, including their clothes and gear, is normal with
a mean of 190 pounds and a standard deviation of 10
pounds. Is the weights of individual passengers are
independent, what is the probability that a group of
four adult male passengers will exceed the acceptable
weight limit of 800 pounds?
A.
B.
C.
D.
E.
0.023
0.046
0.159
0.317
0.977
3. All bags entering a research facility are screened.
Ninety-seven percent of the bags that contain
forbidden material trigger an alarm. Fifteen percent of
the bags that do not contain forbidden material also
trigger the alarm. If 1 out of ever 1,000 bags entering
the building contains forbidden material, what is the
probability that a bag that triggers the alarm will
actually contain forbidden material?
A.
B.
C.
D.
E.
0.00097
0.00640
0.03000
0.14550
0.97000
38. Acme Corporation manufactures light bulbs. The CEO
claims that an average Acme light bulb lasts 300 days.
A researcher randomly selects 15 bulbs for testing.
The sampled bulbs last an average of 290 days, with a
standard deviation of 50 days. If the CEO's claim were
true, what is the probability that 15 randomly
selected bulbs would have an average life of no more
than 290 days?
(A) 0.100
(B) 0.226
(C) 0.334
(D) 0.443
(E) .775
26. Suppose a die is tossed 5 times. What is the
probability of getting exactly 2 fours?
(A) 0.028
(B) 0.161
(C) 0.167
(D) 0.333
(E) There is not enough information to answer
this question.
6. A card is drawn randomly from a deck of
ordinary playing cards. You win $10 if the card
is a spade or an ace. What is the probability
that you will win the game?
(A) 1/13
(B) 13/52
(C) 4/13
(D) 17/52
(E) None of the above.
2. A coin is tossed three times. What is the
probability that it lands on heads exactly one
time?
(A) 0.125
(B) 0.250
(C) 0.333
(D) 0.375
(E) 0.500
30. Bob is a high school basketball player. He is a
70% free throw shooter. That means his
probability of making a free throw is 0.70.
What is the probability that Bob makes his
first free throw on his fifth shot?
(A) 0.0024
(B) 0.0057
(C) 0.0081
(D) 0.0720
(E) 0.1681
31. An archer claims that 25% of her shots will be in the
center of the target (i.e., a bulls-eye). A sports writer
plans to test this claim by sampling 300 shots. If the
300 shots result in 60 or fewer bulls-eyes (i.e., 20%
bulls-eyes), the writer will reject the archer's claim.
What is the probability that the sports writer will reject
the archer's claim, when it is actually true?
(A) 0.01
(B) 0.02
(C) 0.04
(D) 0.08
(E) 0.16
10. Which of the following is a discrete random variable?
I. The average height of a randomly selected group of
boys.
II. The annual number of sweepstakes winners from
New York City.
III. The number of presidential elections in the 20th
century.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
14. The number of adults living in homes on a randomly
selected city block is described by the following probability
distribution.
Number of adults, x : 1
Probability, P(x) :
0.25
2
0.50
3
0.15
4 or more
???
What is the probability that 4 or more adults reside at a
randomly selected home?
(A) 0.10
(B) 0.15
(C) 0.25
(D) 0.50
(E) There is not enough information to answer this
question.
18. The number of adults living in homes on a randomly
selected city block is described by the following
probability distribution.
Number of adults, x: 1
2
3
4
Probability, P(x):
0.25 0.50 0.15 0.10
What is the standard deviation of the probability
distribution?
(A) 0.50
(B) 0.62
(C) 0.79
(D) 0.89
(E) 2.10
11) The XYZ Office Supplies Company sells calculators in bulk at wholesale prices, as
well as individually at retail prices. Next year’s sales depend on market
conditions, but executives use probability to find estimates of sales for the
coming year. The following tables are estimates for next year’s sales.
Wholesale Sales
Number Sold
2,000
5,000
10,000
20,000
Probability
0.1
0.3
0.4
0.2
Retail Sales
Number Sold
600
1,000
1,500
Probability
0.4
0.5
0.1
What profit does XYZ Office Supplies Company expect to make for the next year if the
profit from each calculator sold is $20 at wholesale and $30 at retail?
A.
B.
C.
D.
E.
$10,590
$220,700
264,750
$833,100
$1,002,500
13) Joe and Matthew plan to visit a bookstore. Based on their previous visits to this
bookstore, the probability distributions of the number of books they will buy are
given below.
#of books Joe
will buy
0
1
2
Probability
0.50
0.25
0.25
# of books
Matthew
0
1
2
Probability
0.25
0.50
0.25
Assuming Joe and Matthew make their decisions independently, what is the
probability that they will purchase no books on this visit to the bookstore?
A.
B.
C.
D.
E.
0.0625
0.1250
0.1875
0.2500
0.7500
Every Thursday, Matt and Dave’s Video Venture has “roll the dice” day. A
customer may choose to roll two fair dice and rent a second movie for an
amount (in cents) equal to the numbers uppermost on the dice, with the
larger number first. For example, if the customer rolls a two and a four, a
second movie may be rented for $0.42. If a two and a two are rolled, a
second movie may be rented for $0.22. Let X represent the amount paid
for a second movie on roll-the-dice day. The expected value of X is $0.47
and the standard deviation of X is $0.15.
20) If a customer rolls the dice and rents a second movie every Thursday for
30 consecutive weeks, what is the approximate probability that the total
amount paid for these second movies will exceed $15.00?
A.
B.
C.
D.
E.
0
0.09
0.14
0.86
0.91
23)Circuit boards are assembled by selecting 4
computer chips at random from a large batch of
chips. In this batch of chips, 90 percent of the
chips are acceptable. Let X denote the number
of acceptable chips out of a sample of 4 chips
from this batch. What is the least probable
value of X?
A.
B.
C.
D.
E.
0
1
2
3
4
4) A manufacturer makes lightbulbs and claims that
their reliability is 98 percent. Reliability is defined
to be the proportion of nondefective items that
are produced over the long term. If the
company’s claim is correct, what is the expected
number of nondefective lightbulbs in a random
sample of 1,000 bulbs?
A.
B.
C.
D.
E.
20
200
960
980
1,000
3) A magazine has 1,620,000 subscribers, of whom
640,000 are woman and 980,000 are men. Thirty
percent of the women read the advertisements in the
magazine and 50 percent of the men read the
advertisements in the magazine. A random sample of
100 subscribers is selected. What is the expected
number of subscribers in the sample who read the
advertisements?
A.
B.
C.
D.
E.
30
40
42
50
80
32) The distribution of the weights of loaves of bread
from a certain bakery follows approximately a normal
distribution. Based on a very large sample, it was
found that 10 percent of the loaves weighed less then
15.34 ounces, and 20 percent of the loaves weighed
more than 16.31 ounces. What are the mean and
standard deviation of the distribution of the weights
of the loaves of bread?
A.
B.
C.
D.
E.
μ = 15.82, σ = 0.48
μ = 15.82, σ = 0.69
μ = 15.87, σ = 0.46
μ = 15.93, σ = 0.46
μ = 16.00, σ = 0.50
Unit 6: Sampling Distributions,
Confidence Intervals
•
•
•
•
•
•
Normal distributions
Standard error
Central Limit Theorum
Confidence intervals
Margin of error
Critical values
18. Courtney has constructed a cricket out of paper and rubber bands. According to
the instructions for making the cricket, when it jumps it will land on its feet half
of the time and on its back the other half of the time. In the first 50 jumps,
Courtney’s cricket landed on its feet 35 times. In the next 10 jumps, it landed on
its feet only twice. Based on this experiment, Courtney can conclude that
A.
B.
C.
D.
E.
The cricket was due to land on its feet less than half the time during the final 10
jumps, since it had landed too often on its feet during the first 50 jumps
A confidence interval for estimating the cricket’s true probability of landing on its
feet is wider after the final 10 jumps than it was before the final 10 jumps
A confidence interval for estimating the cricket’s true probability of landing on its
feet after the final 10 jumps is exactly the same as it was before the final 10
jumps
A confidence interval for estimating the cricket’s true probability of landing on its
feet is more narrow after the final 10 jumps than it was before the final 10 jumps
A confidence interval for estimating the cricket’s true probability of landing on its
feet based on the initial 50 jumps does not include 0.2, so there must be a defect
in the cricket’s construction to account for the poor showing in the final 10
jumps
17. A large company is considering opening a franchise in St.
Louis and wants to estimate the mean household income
for the area using a simple random sample of households.
Based on information from a pilot study, the company
assumes that the standard deviation of household
incomes is σ = $7,200. Of the following, which is the least
number of households that should be surveyed to obtain
an estimate that is within $200 of the true mean
household income with 95 percent confidence?
A.
B.
C.
D.
E.
75
1,300
5,200
5,500
7,700
11. The Attila Barbell Company makes bars for weight
lifting. The weights of the bars are independent and
are normally distributed with a mean of 720 ounces
(45 pounds) and a standard deviation of 4 ounces. The
bars are shipped 10 in a box to the retailers. The
weights of the empty boxes are normally distributed
with a mean of 320 ounces and a standard deviation of
8 ounces. The weights of the boxes filled with 10 bars
are expected to be normally distributed with a mean of
7,520 ounces and a standard deviation of
A.
B.
C.
D.
E.
12 ounces
80 ounces
224 ounces
48 ounces
1,664 ounces
4. Which of the following statements is true?
I. When the margin of error is small, the confidence
level is high.
II. When the margin of error is small, the confidence
level is low.
III. A confidence interval is a type of point estimate.
IV. A population mean is an example of a point
estimate.
(A) I only
(B) II only
(C) III only
(D) IV only
(E) None of the above.
7. Which of the following statements is true?
I. The standard error is computed solely from
sample attributes.
II. The standard deviation is computed solely
from sample attributes.
III. The standard error is a measure of central
tendency.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
8. Nine hundred (900) high school freshmen
were randomly selected for a national survey.
Among survey participants, the mean gradepoint average (GPA) was 2.7, and the standard
deviation was 0.4. What is the margin of error,
assuming a 95% confidence level?
(A) 0.013
(B) 0.025
(C) 0.500
(D) 1.960
(E) None of the above.
12. Suppose we want to estimate the average
weight of an adult male in Dekalb County,
Georgia. We draw a random sample of 1,000 men
from a population of 1,000,000 men and weigh
them. We find that the average man in our
sample weighs 180 pounds, and the standard
deviation of the sample is 30 pounds. What is the
95% confidence interval?
(A) 180 + 1.86
(B) 180 + 3.0
(C) 180 + 5.88
(D) 180 + 30
(E) None of the above.
15. A major metropolitan newspaper selected a
simple random sample of 1,600 readers from
their list of 100,000 subscribers. They asked
whether the paper should increase its coverage
of local news. Forty percent of the sample
wanted more local news. What is the 99%
confidence interval for the proportion of readers
who would like more coverage of local news?
(A) 0.30 to 0.50
(B) 0.32 to 0.48
(C) 0.35 to 0.45
(D) 0.37 to 0.43
(E) 0.39 to 0.41
16. Suppose a simple random sample of 150
students is drawn from a population of 3000
college students. Among sampled students,
the average IQ score is 115 with a standard
deviation of 10. What is the 99% confidence
interval for the students' IQ score?
(A) 115 + 0.01
(B) 115 + 0.82
(C) 115 + 2.1
(D) 115 + 2.6
(E) None of the above.
20. Twenty-two students were randomly selected from a population of 1000 students. The
sampling method was simple random sampling. All of the students were given a standardized
English test and a standardized math test. Test results are summarized below.
Studen Englis
t
h
1
95
2
89
3
76
4
92
5
91
6
53
7
67
8
88
9
75
10
85
11
90
Math
90
85
73
90
90
53
68
90
78
89
95
Differe
(d - d)2
nce, d
5
16
4
9
3
4
2
1
1
0
0
1
-1
4
-2
9
-3
16
-4
25
-5
36
Student English Math
12
13
14
15
16
17
18
19
20
21
22
85
87
85
85
68
81
84
71
46
75
80
83
83
83
82
65
79
83
60
47
77
83
Differen
ce, d
2
4
2
3
3
2
1
11
-1
-2
-3
(d - d)2
1
9
1
4
4
1
0
100
4
9
16
Σ(d - d)2 = 270
d=1
What is the 90% confidence interval for the mean difference between student scores on the math and English tests? Assume
that the mean differences are approximately normally distributed.
(A) 1 + 0.8
(B) 1 + 1.0
(C) 1 + 1.3
(D) 1 + 2.0
(E) 1 + 3.6
16) Ten students were randomly selected from a high school students to take
part in a program designed to raise their reading comprehension. Each
students took a test before and after completing the program. The
mean of the differences between the score after the program and the
score before the program is 16. It was decided that all students in the
school would take part in this program during the next school year. Let
uA denote the mean score after the program and uB denote the mean
score before the program for all students in the school. The 95 percent
confidence interval estimate of the true mean difference for all students
Is (9, 23). Which of the following statements is a correct interpretation
of this confidence interval?
A. uA > uB with probability 0.95.
B. uA < uB with probability 0.95.
C. uA is around 23 and uB is around 9.
D. For any uA and uB with (uA – uB) ≥ 14, the sample result is quite likely.
E. For any uA and uB with 9 < (uA – uB) < 23, the sample result is quite
likely.
24)A random sample of the costs of repair jobs at a
large muffler repair shop produces a mean of
$127.95 and a standard deviation of $24.03. If
the size of this sample is 40, which of the
following is an approximate 90 percent
confidence interval for the average cost of a
repair at this repair shop?
A.
B.
C.
D.
E.
$127.95 +/= $4.87
$127.95 +/= $6.24
$127.95 +/= $7.45
$127.95 +/= $30.81
$127.95 +/= $39.53
33)A 95 percent confidence interval of the form p
+/= E will be used to obtain an estimate for an
unknown population proportion p. If p is the
sample proportion and E is the margin of error,
which of the following is the smallest sample
size that will guarantee a margin of error of at
most 0.08?
A.
B.
C.
D.
E.
25
100
175
250
625
35) A survey was conducted to determine what
percentage of college seniors would have chosen to
attend a different college if they had known what
they know now. In a random sample of 100 seniors,
34 percent indicated that they would have attended a
different college. A 90 percent confidence interval for
the percentage of all seniors who would have
attended a different college is
A.
B.
C.
D.
E.
24.7% to 43.3%
25.8% to 42.2%
26.2% to 41.8%
30.6% to 37.4%
31.2% to 36.8%
1) USA Today reported that speed skater Bonnie Blair had
“won the USA’s heart , according to a poll conducted on the
final day of the 1994 Winter Olympics. When asked who
was the hero of the Olympics, 65 percent of the
respondents chose Blair, who won five fold medals. The poll
of 615 adults, done by telephone, had a margin of error of 4
percent. Which of the following statements best describes
what is meant by the 4 percent margin of error?
A. About 4 percent of adults were expected to change their
minds between the time of the poll and its publication in
USA Today.
B. About 4 percent of adults did not have telephones.
C. About 4 percent of the 615 adults polled refused to answer.
D. Not all of the 615 adults knew anything about the Olympics.
E. The difference between the sample percentage and the
population percentage is likely to be less than 4 percent.
7)
A certain country has 1,000 farms. Corn is grown on 100 of these farms but on
none of the others. In order to estimate the total farm acreage of corn for the
country, two plans are proposed.
Plan 1: (a) Sample 20 farms at random
(b) Estimate the mean acreage of corn per farm in a
confidence interval
(c) Multiply both ends of the interval by 1,000 to get an
interval estimate of the total.
Plan 2: (a) Identify the 100 corn-growing farms.
(b) Sample 20 corn-growing farms at random
(c) Estimate the mean acreage of corn for corn-growing
farms in a confidence interval.
(d) Multiply both ends of the interval by 100 to get an
interval estimate of the total.
On the basis of the information given, which of the following is the better method
for estimating the total farm acreage of corn for the country?
A. Choose plan I over plan II.
B. Choose plan II over plan I.
C. Choose either plan, since both are good and will produce equivalent results.
D. Choose neither plan, since neither estimates the total farm acreage of corn.
E. The plans cannot be evaluated from the information given.
Unit 7: Hypothesis Testing
• 2c. Select and use appropriate statistical
methods in decision-making and hypothesis
testing. (DOK 2)
• Significance levels
• Types of errors
• P-value
15. The mayor of a large city will run for governor if he believes that
more than 30 percent of the voters in the state already support
him. He will have a survey firm ask a random sample of n voters
whether or not they support him. He will use a large sample test
for proportions to test the null hypothesis that the proportion of
all voters who support him is 30 percent or less against the
alternative that the percentage is higher than 30 percent.
Suppose that 35 percent of all voters in the state actually support
him. In which of the following situations would the power for this
test be highest?
A.
B.
C.
D.
E.
The mayor uses a significance level of 0.01 and n = 250 voters.
The mayor uses a significance level of 0.01 and n = 500 voters.
The mayor uses a significance level of 0.01 and n = 1,000 voters.
The mayor uses a significance level of 0.05 and n = 500 voters.
The mayor uses a significance level of 0.05 and n = 1,000 voters.
28. In hypothesis testing, which of the following
statements are always true?
I. The P-value is greater than the significance level.
II. The P-value is computed from the significance level.
III. The P-value is the parameter in the null hypothesis.
IV. The P-value is a test statistic.
V. The P-value is a probability.
(A) I only
(B) II only
(C) III only
(D) IV only
(E) V only
24. Suppose a researcher conducts an experiment
to test a hypothesis. If she doubles her sample
size, which of the following will increase?
I. The power of the hypothesis test.
II. The effect size of the hypothesis test.
III. The probability of making a Type II error.
(A) I only
(B) II only
(C) III only
(D) All of the above
(E) None of the above
32.The Acme Car Company claims that at most 8%
of its new cars have a manufacturing defect. A
quality control inspector randomly selects 300
new cars and finds that 33 have a defect. Should
she reject the 8% claim? Assume that the
significance level is 0.05.
(A) Yes, because the P-value is 0.016.
(B) Yes, because the P-value is 0.028.
(C) No, because the P-value is 0.16.
(D) No, because the P-value is 0.28.
(E) There is not enough information to reach a
conclusion.
36. A sports writer hypothesized that Tiger Woods plays better on par
3 holes than on par 4 holes. He reviewed Woods' performance in
a random sample of golf tournaments. On the par 3 holes, Woods
made a birdie in 20 out of 80 attempts. On the par 4 holes, he
made a birdie in 40 out of 200 attempts. How would you interpret
this result?
(A) The P-value is < 0.001, very strong evidence that Woods plays
better on par 3 holes.
(B) The P-value is between 0.001 and 0.01, strong evidence that
Woods plays better on par 3 holes.
(C) The P-value is between 0.01 and 0.05, moderate evidence that
Woods plays better on par 3 holes.
(D) The P-value is between 0.05 and 0.10, some evidence that
Woods plays better on par 3 holes.
(E) The P-value is > 0.10, little or no support for the notion that
Woods plays better on par 3 holes.
39. Which of the following would be a reason to use a
one-sample t-test instead of a one-sample z-test?
I. The standard deviation of the population is unknown.
II. The null hypothesis involves a continuous variable.
III. The sample size is large (greater than 40).
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
2) An automobile manufacturer claims that the
average gas mileage of a new model is 35 miles
per gallon (mpg). A consumer group is skeptical
of this claim and thinks the manufacturer may be
overstating the average gas mileage. If u
represents the true average gas mileage for this
new model, which of the following gives the null
and alternative hypotheses that the consumer
group should test?
A. H0: μ < 35 mpg, Ha: μ ≥ 35 mpg
B. H0: μ ≤ 35 mpg, Ha: μ > 35 mpg
C. H0: μ = 35 mpg, Ha: μ > 35 mpg
D. H0: μ = 35 mpg, Ha: μ < 35 mpg
E. H0: μ = 35 mpg, Ha: μ ≠ 35mpg
29) In a test of the null hypothesis H0: u = 10 against the
alternative hypothesis Ha: u > 10, a sample from a
normal population produces a mean of 13.4. The zscore for the sample is 2.12 and the p-value is 0.017.
Based on these statistics, which of the following
conclusions could be drawn?
A. There is no reason to conclude that u > 10.
B. Due to random fluctuation, 48.3 percent of the
time a sample produces a mean larger than 10.
C. 1.7 percent of the time, rejecting the alternative
hypothesis is in error.
D. 1.7 percent of the time, the mean is above 10.
E. 98.3 percent of the time, the mean is below 10.
34) The process of producing pain-reliever tablets yields
tablets with varying amounts of the active ingredient.
It is claimed that the average amount of active
ingredient per tablet is at least 200 milligrams. The
Consumer Watchdog Bureau tests a random sample
of 70 tablets. The mean content of the active
ingredient for this sample is 194.3 milligrams, while
the standard deviation is 21 milligrams. What is the
approximate p-value for the appropriate test?
A.
B.
C.
D.
E.
0.012
0.024
0.050
0.100
0.488
6. In a test of H0: μ = 8 versus Ha: μ ≠ 8, a sample of size
220 leads to a p-value of 0.034. Which of the
following must be true?
A. A 95% confidence interval for μ calculated from
these data will not include μ = 8.
B. At the 5% level is H0 is rejected, the probability of a
Type II error is 0.034.
C. The 95% confidence interval for μ calculated from
these data will be centered at μ = 8.
D. The null hypothesis should not be rejected at the
5% level.
E. The sample size is insufficient to draw a conclusion
with 95% confidence.
Unit 8
• Degrees of freedom
• T-values
• Chi-squared tests
23. Acme Toy Company sells baseball cards in packages of 100.
Three types of players are represented in each package -rookies, veterans, and All-Stars. The company claims that
30% of the cards are rookies, 60% are veterans, and 10%
are All-Stars. Cards from each group are randomly assigned
to packages.
Suppose you bought a package of cards and counted the
players from each group. What method would you use to
test Acme's claim that 30% of the production run are
rookies; 60%, veterans; and 10%, All-Stars.
(A) Chi-square goodness of fit test
(B) Chi-square test for homogeneity
(C) Chi-square test for independence
(D) One-sample t test
(E) Matched pairs t-test
40. A public opinion poll surveyed a simple random sample of voters.
Respondents were classified by gender (male or female) and by voting
preference (Republican, Democrat, or Independent). Results are shown
below.
Voting Preferences
Republican
Democrat
Independent
Row total
Male
200
150
50
400
Female
250
300
50
600
Column total
450
450
100
1000
If you conduct a chi-square test of independence, what is the expected
frequency count of male Independents?
(A) 40
(B) 50
(C) 60
(D) 180
(E) 270
5) When a virus is placed on a tobacco leaf, small lesions appear on the leaf.
To compare the mean number of lesions produced by 2 different strains of
virus, one strain is applied to half of each of 8 tobacco leaves, and the
other strain is applied to the other half of each leaf. The strain that goes
on the right half of the leaf is decided by a coin flip. The lesions that
appear on each half are then counted. The data are given below.
Leaf
1
2
3
4
5
6
7
8
Strain 1
31
20
18
17
9
8
10
7
Strain 2
18
17
14
11
10
7
5
6
What is the number of degrees of freedom associated with the appropriate ttest for testing to see if there is a difference between the mean number of
lesions per leaf produced by the two strains?
A. 7
B. 8
C. 11
D. 14
E. 16
6) Which of the following is a criterion for
choosing a t-test rather than a z-test when
making an inference about the mean of a
population?
A. The standard deviation of the population is
unknown.
B. The mean of the population is unknown.
C. The sample may not have been a simple
random sample.
D. The population is not normally distributed.
E. The sample size is less than 100.
4. A candy company claims that 10 percent of its
candies are blue. A random sample of 200 of
these candies is taken, and 16 are found to be
blue. Which of the following tests would be
most appropriate for establishing whether the
candy company needs to change its claim?
A.
B.
C.
D.
E.
Matched pairs t-test
One-sample proportion test
Two-sample t-test
Two-sample proportion z-test
Chi-squared test of association
13.
An investigator was studying a territorial species of Central American termites, Nasutitermes
corniger. Forty-nine termite pairs were randomly selected; both members of each of these pairs
were from the same colony. Fifty-five additional termite pairs were randomly selected; the two
members in each of these pairs were from different colonies. The pairs were placed in petri
dishes and observed to see whether they exhibited aggressive behavior. The results are shown in
the table below.
Aggressive
Nonaggressive
Total
Same colony
40 (33.5)
9 (15.5)
49
Different Colonies
31 (37.5)
24 (17.5)
55
Total
71
33
104
A Chi-squared test for homogeneity was conducted, resulting in X2 = 7.638. The expected counts
are shown in parentheses in the table. Which of the following sets of statements follows from
these results?
A.
B.
C.
D.
E.
X2 is not significant at the 0.05 level.
X2 is significant, 0.01 < p < 0.05; the counts in the table suggest that termite pairs from the same
colony are less likely to be aggressive than termite pairs from different colonies.
X2 is significant, 0.01 < p < 0.05; the counts in the table suggest that termite pairs from different
colonies are less likely to be aggressive than termite pairs from the same colony.
X2 is significant, p < 0.01; the counts in the table suggest that termite pairs from the same colony
are less likely to be aggressive than termite pairs from different colonies.
X2 is significant, p < 0.01; the counts in the table suggest that termite pairs from different colonies
are less likely to be aggressive than termite pairs from the same colony.