AP Statistics Exam Review
Topic I: Describing Data
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Use the given data set of test grades from a college statistics class for this question.
85 72 64 65 98 78 75 76 82 80 61 92 72 58 65 74 92 85 74 76 77 77 62 68 68 54 62 76 73 85 88 91 99 82 80
74 76 77 70 60
A.
Construct two different graphs of these data
B.
Calculate the five-number summary and the mean and standard deviation of the data.
C.
Describe the distribution of the data, citing both the plots and the summary statistics found in questions 1
and 2.
AP Statistics Exam Review
Topic II: Normal Distribution
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A set of 2,000 measurements had a symmetric, mound-shaped distribution. The mean is 5.3 and the standard
deviation is 0.7. Determine an interval that contains approximately 1,360 date values.
AP Statistics Exam Review
Topic III: Bivariate Data
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A survey was conducted recently in ten large American cities to determine whether there is any relationship
between the average weekday hotel rates and average car rental rates. The following data was collected.
Daily Hotel Rate
(x) (in dollars)
149
187
171
122
115
147
128
212
168
181
A.
B.
C.
D.
E.
Daily Car Rental Rate
(y) (in dollars)
49
50
52
49
39
44
37
63
46
51
Construct a scatterplot for this data
Use the scatterplot to determine if there is a linear relationship between the two variables
If there is a linear relationship, numerically describe the strength of this relationship and construct a least
squares regression model
Find the residual associated with the point (168, 46).
What percent of the variation in the car rental rates is explained by the regression of y on x?
AP Statistics Exam Review
Topic IV: Planning a Study
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The loss of bone mass density (BMD) in men and women can be reduced by drug treatments. A pharmaceutical
company has developed a new calcium supplement, which claims to reduce the loss of BMD. Volunteers who have
been diagnosed with loss of bone mass density and who are currently not on medication or calcium supplements will
be recruited to participate in a study. It is known that men and women experience different average losses of
BMD.
A.
B.
C.
Explain how you would carry out a completely randomized experiment for the study.
Describe an experimental design that would improve the design in part (A) by incorporating blocking.
Can the experimental design in part (B) be carried out in a double-blind manner? Explain.
AP Statistics Exam Review
Topic V: Probability
A. 12
B. 16
C. 24
D. 48
E. 144
A. 0.40
B. 0.42
C. 0.46
D. 0.05
E. 0.52
A. 1/8
B. ¼
C. 1/2
D. 2/3
E. 1/16
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A telecommunications company uses three different systems to produce the print shaft holder for its most popular
fax machine. System A produces 50% of the shaft holders, System B produces 30% of the shaft holders, and
System C produces 20% of the shaft holders. The percentages of the defective shaft holders produced by each
system are respectively, 3%, 4% and 5%.
A.
B.
If a shaft holder is selected at random, what is the probability that it is defective?
If a shaft holder is selected at random and found to be defective, what is the probability that it was
produced by System A?
AP Statistics Exam Review
Topic VI: Binomial Situations and Sampling Distributions
A. 0.029
B. 0.020
C. 0.041
D. 0.032
E. 0.023
A. 0.9123
B. 0.9029
C. 0.9332
D. 0.0233
E. 0.1093
A. 6
B. 30
C. 20
D. 120 E. 60
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A breakfast cereal manufacturer has an incentive program for people to buy its product: in each box of cereal, one
picture of a baseball superstar is included. Any one of five different pictures can be enclosed in the boxes and the
total number of pictures of each superstar is the same. You are interested only in finding a picture of Babe Ruth.
In each case, show the formula you use, the substitution into it and the answer.
A.
B.
Find the probability that you get your first picture of Babe Ruth in the 2 nd box that you buy.
Find the probability that you get your first picture of Babe Ruth in the 10 th box that you buy.
AP Statistics Exam Review
Topic VII: Confidence Intervals and Significance Testing
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I.
An educational group claims that teaching fraction concepts using math manipulatives results in higher
student achievement and understanding of fractions than teaching fractions without the use of any math
manipulatives. A teacher in a middle school taught a unit on fractions to two sixth grade classes, one using
math manipulatives and the other without the use of any manipulatives. The table below shows the
performance of these two classes on a unit test on fractions.
With Manipulatives
85
75
83
87
80
79
88
94
87
82
Without Manipulatives
78
84
81
78
76
83
79
75
85
81
Test the claim that students who use manipulatives show higher achievement on a test of fractions. Give
appropriate statistical evidence to support your answer.
II.
A county legislator is interested in polling her constituents to estimate the difference between the
positions of men and women regarding a proposed bill to restrict cell phone use while driving. Her
administrative assistants draw two samples, one consisting of 500 men and the other consisting of 500
women. The survey indicates that 230 men and 194 women favor legislation that would restrict the use of
cell phones while driving.
A.
Construct a 95% confidence interval to estimate the true difference between the proportions of
men and women who favor legislation that restricts cell phone use while driving. Explain how you
arrived at your solution and explain your reasons for selecting the type of confidence interval that
you chose.
B.
Write one or two statements to a non-statistician explaining what is meant by the 95% confidence
interval found in part (A)
C.
How does a 99% confidence interval for the same data compare to the 95% confidence interval?
Interpret your response in the context of this problem.
AP Statistics Exam Review
Topic VIII: Other Models of Inference
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A medical research team is conducting a study to determine whether there is a relationships between aerobic
walking and cholesterol levels. A random sample of 315 subjects is selected and represented in the table below.
Test the claim that aerobic walking and cholesterol levels are related. Include appropriate statistical evidence to
support your findings.
Walkers
Non-Walkers
Low
51
23
Average
86
94
Elevated
31
30
SOLUTIONS
Topic I: Describing Data
A.
B.
C.
It appears from both the graphical displays and the summary
statistics indicated that the data are symmetric and unimodal.
There is a slight skew to the right
Topic II: Normal Distribution
1,360/ 2,000 is 68% of the data. Therefore, using the empirical rule,
an interval within one standard deviation of the mean should have
approximately 68% of the data: an approximate interval is
(5.3 - 0.7, 5.3 + 0.7) = (4.6, 6.0)
Topic III: Bivariate Data
A.
x= daily hotel rate in dollars
y= daily car rental rate in dollars
B.
There is a moderate to strong positive linear relationship
between daily hotel rates in dollars and the daily car rental
rates in dollars.
C.
D.
E.
The correlation coefficient is r= 0.82.
The least squares regression model is y-hat= 17.75 + 0.1914x.
The residual associated with the point (168, 46) can be found
by the finding the predicted value of y by substituting x= 168
into the regression model.
y-hat= 17.75 + 0.1914 (168)
y-hat= 49.9
Residual = observed minus the predicted Residual = 46- 49.9
Residual= -3.9
r 2  0.675
Topic IV: Planning a Study
A.
Throw the names of the volunteers in a hat or use some other random
assignment method such as a random digit table and randomly assign
volunteers
to two different groups, a control group and a treatment group. The
treatment group would receive the supplement. The control group would
receive another type of supplement already in use. Compare the results of the
two groups at the end.
B.
Identify group A as the new medicine group and group B as the control group.
Since men and women experience different levels of BMD loss, separate men
and women first. Then randomly assign members of each gender into Group A
or Group B. Compare the results within each gender.
Group A
Group B
Men
Volunteers
Group A
Women
Group B
C.
Compare
Results
Compare
Results
Yes, as long as the subjects do not know whether they are receiving the
treatment or the placebo and the researcher administering and monitoring the
experiment also does not know which one the subjects are receiving. Then the
experiment would be double blind.
Topic V: Probability
3%
System A
97 %
Defective
Not Defective
50%
4%
30%
Defective
System B
96 %
Not Defective
20%
System C
5%
95 %
A.
Defective
Not Defective
P(Defective) = 0.5(0.03)  0.3(0.04)  0.2(0.05)  0.037
B.
P(System A given that it is defective) =
Topic VI: Binomial Situations and Sampling Distributions
A.
This is a geometric distribution.
P (X  n )  p (1  p )n 1 where the first success occurs on the nth
trial.
P (x  2)  (0.2)(1  0.2)21  0.16
B.
.05(0.03)
 0.405
0.037
P (x  10)  (0.2)(1  0.2)101  0.0268
Topic VII: Confidence Intervals and Significance Testing
1.
The test required for this problem is a two sample difference of
means t-test since the groups are independent and since σ is
unknown. The test requires the two samples to be independently
selected simple random samples and for the two populations to be
normally distributed. It is not verified how these classes are
selected, so we will assume that we have 2 independent SRSs.
Checking for normality we will use normal quantile plots:
2.
A.
Because we have two independent random samples from two
distinct populations (men and women) and we are looking to see the
difference between the proportion of men and women who favor
legislation which restrict cell phone use while driving, the choice of
interval would be a two proportion confidence interval:


pˆm  pˆw  z *
pˆm (1  pˆm ) pˆw (1  pˆw )

nm
nw
Assumptions include
two independent random samples from large populations. We will
assume that there are at least 5000 men and 5000 women in the
country. Our counts of successes and failures all have to be large
ˆm
enough. ( nm p


 5,nm (1  pˆm )  5,nw pˆw  5,nw 1  pˆw  5 )
All
of the conditions are satisfied.
230
230
194
194
(1 
)
(1 
)
 230 194 
500
500
500
500



  1.96
500
500
500
500


(0.0109, 0.1331)
B. We are 95% confident that the difference in population
proportions is between 0.0109 and 0.1331. Because the interval does
not contain 0, we are confident tht the men have a stronger
preference for legislation that would restrict the use of cell phones
while driving.
C. A 99% confidence interval would change the value of z* in the
formula above from 1.96 to 2.576 thus making the interval wider.
The new interval would become (-0.0083, 0.15229). This wider
interval would contain 0 and the conclusion reached concerning
whether there is a difference in the proportion of men and women
who favored legislation would be different in part A. i.e. there would
appear to be no statistically significance difference between the two
groups.
Topic VIII: Other Models of Inference