AP Statistics Practice Exam
AP Statistics Practice Exam
AP Statistics Practice Exam
Page 1 of 19
Mixed Practice with Multiple-Choice and Free-Response Questions
Study Sheet
Multiple-Choice Section
Choose the one best answer for each of the following questions.
1. The probability of getting a specific grade in freshman English is given in
the table below. Each letter grade has a specific number of grade points
associated with it. What is the GPA (grade point average) in freshman
English?
Grade
Grade
Points
Probability
A.
2.0
B.
2.1
C.
1.9
A
4
B
3
C
2
D
1
F
0
.05
.3
.3
.2
.15
D. 1.8
E.
2.25
2. A 99% confidence interval for the proportion of voters who favor a ballot
initiative to lower property taxes is (.68, .76). Which of the following
statements are true?
I. The probability is .99 that between 68% and 76% of voters will vote to
lower property taxes.
II. The procedure used to generate this interval will contain the true
population proportion 99% of the time.
III. About 99% of those responding are in favor of lowering property taxes.
A.
I only
B.
II only
C.
III only
D. I and II only
E.
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.300
B.
.288
C.
.294
D. .290
E.
.304
B.
D.
C.
E.
B.
Using blocks when experimental units are known to be similar in some way
C.
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I only
B.
II only
C.
III only
7. An advertisement for a weight loss clinic claims that people who go through
the complete program lose an average of 75 lb. A statistician finds that, at
the .05 level of significance, if the true weight loss is actually equal to 71 lb,
then the power against the claim of 75 lb is .80. Which of the following
statements best explains what this means?
A.
The probability that the true mean weight loss is 71 lb or less is .8.
B.
If the true average weight loss is 71 lb, the probability of rejecting the claim that
it is 75 is .80.
C.
There is a .05 chance of getting a value as deviant as 71 if the true mean weight
loss is really 75 lb.
D. There is a .8 chance of rejecting the claim that the true mean weight loss is 75
lb if a sample value of 71 lb is obtained.
E.
If the true mean weight loss is 71 lb, the probability of getting a finding as large
as 75 lb is .80.
15
B.
60
C.
30
D. 45
E.
225
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I only
B.
II only
C.
III only
B.
C.
11. A sample of the ages of the teachers at a local high school is composed of
the following values: 34, 35, 32, 38, 45, 56, 42, 35, 44, 47. You want to use
these data to generate a 90% confidence interval for the population mean.
What is the upper critical t value (t*) you would use?
A.
1.812
B.
1.372
C.
1.383
D. 1.833
E.
1.860
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31, 81
B.
32, 81
C.
31, 80
D. 32, 80
E.
33, 86
13. In the game of Chuck-a-Luck, you select a number between 1 and 6, then
roll three dice. You win 1 point for each die showing your number. You lose
a point only if your number fails to come up on any of the three dice. Thus,
in a single turn, you can win 1, 2, or 3 points, or you can lose 1 point. What
is the probability that you will win at least 1 point in a single turn?
A.
75/216
B.
3/4
C.
1/4
D. 125/216
E.
91/216
14. To select three rats from a group of ten, you decide to use the following set
gathered from a table of random numbers: 11793 20495 05907 11384
44982 20751 27498. The rats, named Al, Betty, Chuck, Diane, Ernie, Fran,
Guy, Helen, Ira, and Jean, are numbered 1 to 10, respectively. If you started
from the left of your number set, which of these groups of rats would you
select?
A.
117
B.
C.
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289
B.
385
C.
256
D. 384
E.
1,537
.0029
B.
.054
C.
.049
D. .057
E.
.544
17. The following regression equation is used to predict College GPA based on
High School GPA: College GPA = .29 + .98(High School GPA). The residual
when the High School GPA is 3.1 is .052. What is the actual value of the
College GPA when the High School GPA equals 3.1?
A.
2.6
B.
2.9
C.
3.0
D. 2.7
E.
2.8
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.336; .024
B.
.336; .128
C.
.336; .664
D. .664; .024
E.
.664; .128
19. Which of the following statements about r, the correlation coefficient, are
true?
I. Given a set of data ( x i , y i ), the correlation coefficient is the same as
the data set we would get if we reversed each x and y value.
II. Consider a bivariate data set ( x i , y i ), and a corresponding data set,
( z xi , z yi ), made up of the z-scores of the original data. For the set
( z xi , z yi ), r = the slope of the regression line.
III. r 2 represents the proportion of the variation in the dependent variable
explained by the regression on the independent variable.
A.
I only
B.
II only
C.
III only
B.
2.24
C.
1.55
0
.17
2
.30
3
.21
4
.08
D. 2.08
E.
1.79
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I only
B.
II only
C.
III only
I and II only
22. You construct a confidence interval for the difference between two
population means. Which of the following statements are true?
I. Unless we are justified in pooling our estimates of the population
variance, this distribution is only approximated by a t distribution.
II. Unlike procedures for a single mean, which require t procedures,
z-procedures are usually appropriate for the difference between two
means.
III. If there is some third variable that exerts an explanatory influence on
both variables whose means are being estimated, we are dealing with
one-sample rather than two-sample procedures.
A.
I only
B.
II only
C.
III only
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12; 2
B.
12; 5
C.
12; 7
D. 9; 2
E.
9; 5
X + Y = 2X + Y2 .
A.
I only
B.
II only
C.
III only
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The sample proportion agreeing with the statement would probably be less than
the true population proportion supporting the amendment.
B.
Within normal limits of variation, the sample proportion agreeing with the
statement would probably be very close to the true population proportion
supporting the amendment.
C.
The sample proportion agreeing with the statement would probably be greater
than the true population proportion supporting the amendment.
Since the sample size is not specified, it is not possible to predict the direction of
bias, if any.
26. Farley's score on his first statistics test of the year was 58. The scores for
the entire class were normally distributed with a mean of 65 and a standard
deviation of 5. His score on the second statistics test of the year was 70, but
this was an easier test and the class average was 78 with a standard
deviation of 6. Which of the following statements is true?
A.
Farley is improving in relation to the rest of the class because his score went up.
B.
C.
Farley did better on the first test because his z-score was greater.
D. Farley did better on the first test because he was not as far away from the class
average.
E.
In relation to the rest of the class, Farley did equally well on both tests.
B.
C.
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A.
.333
B.
.15
C.
.265
1
.1
2
.1
3
.15
4
.20
5
.20
6
.25
D. .122
E.
.58
29. You are designing a survey and plan to draw a simple random sample from
a well-defined population, but are worried that the sample you have in mind
might have more variability than you want. Which of the following would
help control for the amount of variability in the sample?
I. Increase the sample size.
II. Stratify your sample to make sure each group of interest is
proportionately represented.
III. Simplify the wording of the questions in your survey.
A.
I only
B.
I and II only
C.
II only
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A.
The correlation would be weaker and the slope of the regression line would be
closer to 1.
B.
The correlation would be stronger and the slope of the regression line would be
closer to 1.
C.
The correlation would be stronger and the slope of the regression line would be
closer to 1.
D. The correlation would be weaker and the slope of the regression line would be
closer to 1.
E.
Both the correlation coefficient and the slope of the regression line would be
closer to 0.
31. The table shown below gives the observed values for a 2 test of
independence. What is the expected value for the cell in the fourth row,
second column (the cell with the "10" in it)?
15
12
18
15
14
A.
11.0
B.
9.8
C.
10.6
8
12
9
10
12
D. 10.2
E.
9.4
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11.34
B.
.296
C.
.21
y
2
5
11
14
30
34
ln y
.69315
1.60944
2.39790
2.63906
3.40120
3.52636
D. .296
E.
.021
33. You find the correlation coefficient between two variables to be .90. You
may conclude that:
A.
high values of the explanatory variable are associated with low values of the
response variable.
B.
C.
low values of the explanatory variable are associated with low values of the
response variable.
high values of the explanatory variable are associated with high values of the
response variable.
B.
C.
Systematic sample
D. Judgement sample
E.
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Age
Predictor
Constant
Age
s = 1.451
Coef
34.6795
4.2179
R-sq = 97.1%
A.
4.22 3.169(.232)
B.
4.22 3.103(.232)
C.
4.22 3.169(1.451)
Stdev
0.9150
0.2324
t-ratio
37.90
18.15
p
0.000
0.000
R-sq(adj) = 96.8%
D. 4.22 3.103(1.451)
E.
34.68 3.169(.232)
36. Referring to the computer output shown here, which of the following
statements are true?
I. The standard error of the slope of the regression line is .2324.
II. There appears to be a statistically significant relationship between
"Age" and "Value."
III. The standard error of the residuals is 1.451.
Regression Analysis
Age
Predictor
Constant
Age
s = 1.451
A.
I only
B.
II only
C.
III only
Coef
34.6795
4.2179
R-sq = 97.1%
Stdev
0.9150
0.2324
t-ratio
37.90
18.15
p
0.000
0.000
R-sq(adj) = 96.8%
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36
B.
C.
1,296
D. 216
E.
144
38. You roll two dice, A and B. What is the probability that both dice show the
same number given that one of the dice shows a 3 or larger? (Use the table
shown here to help you find your answer.)
A2
B1
(1, 1)
(2, 1)
B2
(1, 2)
(2, 2)
B3
(1, 3)
(2, 3)
B4
(1, 4)
(2, 4)
B5
(1, 5)
(2, 5)
B6
(1, 6)
(2, 6)
A3
A4
A5
A6
(3, 1)
(4, 1)
(5, 1)
(6 ,1)
(3,
(4,
(5,
(6,
(3,
(4,
(5,
(6,
(3,
(4,
(5,
(6,
(3,
(4,
(5,
(6,
(3,
(4,
(5,
(6,
A1
A.
8/9
B.
1/8
C.
1/9
2)
2)
2)
2)
3)
3)
3)
3)
4)
4)
4)
4)
5)
5)
5)
5)
6)
6)
6)
6)
D. 1/16
E.
1/4
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A1
A2
A3
A4
A5
A6
A.
11/36
B.
1/6
C.
1/11
B1
(1, 1)
(2, 1)
(3, 1)
(4, 1)
(5, 1)
(6, 1)
B2
(1, 2)
(2, 2)
(3, 2)
(4, 2)
(5, 2)
(6, 2)
B3
(1, 3)
(2, 3)
(3, 3)
(4, 3)
(5, 3)
(6, 3)
B4
(1, 4)
(2, 4)
(3, 4)
(4, 4)
(5, 4)
(6, 4)
B5
(1, 5)
(2, 5)
(3, 5)
(4, 5)
(5, 5)
(6, 5)
B6
(1, 6)
(2, 6)
(3, 6)
(4, 6)
(5, 6)
(6, 6)
D. 6/11
E.
1/2
40. You collect data on two independent random samples from normal
populations. You conduct a two-sided hypothesis test and pool the
estimates of the population variance. The data are: x1 = 17.5, s x1 = 1.33,
n1 = 28, x 2 = 18.2, s x2 = 1.48, n2 = 30, s p = 1.40, s x1 x2 = .37. What is
the value of t for this test and what is the corresponding P-value?
A.
B.
C.
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40
12
C
U
M
R
E
L
F
R
E
Q
B.
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
3
4
5
NUMBER OF ATTEMPTS
What are the mean and median number of attempts needed to pass the bar
for these 75 lawyers?
2. As research director for a drug company, you want to determine the effectiveness of
a new treatment for arthritis. You suspect that the drug might have different effects
at different treatment levels (the levels under consideration are 350 mg and 500
mg). You also suspect that men and women might react differently to the
medication, and that people 60 and over might experience different effects than
those under 60. You have available to you 180 volunteers who suffer from arthritis.
Exactly half of these volunteers are men and half are women, and exactly half of the
volunteers are 60 years old or older.
A.
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3. Researchers conduct a program to improve the mathematical skill of noncollege math majors of 12 volunteers. The math skills of the volunteers are
evaluated before and after the training. The results are as follows:
Subject
Archie
Betty
Chuck
Dolores
Eddie
Fran
George
Helen
Irving
Janice
Ken
Loretta
Pre-test
56
63
72
59
58
65
61
74
52
60
60
79
Post-test
58
62
75
61
57
69
63
74
54
58
64
80
Does this provide evidence that the program was effective in improving
mathematics skill for these subjects? Use good statistical reasoning in your
answer.
4. The California State Lottery "Pick 6" game allows you to pick six different numbers
from 1 through 51. A machine randomly picks six different numbers from 1 through
51 (once a number is chosen, it is not returned to the box and cannot be chosen
again). You can win money if you match at least 3 of the numbers. Let X = the
amount of numbers that you match.
A. What is P(X = 6)? That is, what is the probability that you match all six
numbers? Provide an understandable explanation.
B. Consider a variation of this game in which each number could be repeated.
That is, once a ball is drawn with a number on it, it is returned to the box
and can be drawn again. What is the probability that you will get at least
one match in the first 5 drawings?
C. What is the probability that the first match comes on the fifth drawing?
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Frequency
17
41
80
134
118
71
24
13
2
TI-83 screens are used with the permission of the publisher. Copyright 1996, Texas
Instruments, Incorporated.
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