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... and for the AP® Statistics Exam

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the AP ® Statistics exam.
604 UNIT 6 Inference for Categorical Data: Proportions

UNIT 6, PART I AP® STATISTICS PRACTICE TEST
Each Unit/Part concludes with an
®
AP STATISTICS PRACTICE TEST Section I: Multiple Choice Select the best answer for each question.
that usually consists of 10 multiple- T1 A confidence interval for a proportion is 0.272 to (A) 0.05 (D) 0.40
0.314. What are the point estimate and the margin of (B) 0.10 (E) 0.90
choice questions and 3 free-response error for this interval? (C) 0.20
(A) 0.293, 0.021 (D) 0.586, 0.021
questions. (B) 0.293, 0.042 (E) 0.586, 0.042 T5 Bags of a certain brand of tortilla chips are labeled
UNIT 6 Inference for Categorical Data: Proportions
606
(C) 0.293, 0.084 as having a net weight of 14 ounces. A representative
of a consumer advocacy group wishes to see if there
T2 Many television viewers express doubts about the valid- is convincing evidence that the mean net weight is
Section II: Free Response Show all your work. Indicate clearly the methods you use, because you will be graded on
ity of certain commercials. In an attempt to answer its less than advertised and so intends to test H : 0 µ = 14 315
CUMULATIVE AP® PRACTICE TEST 1
the correctness of your methods as well as on the accuracy and completeness of your results and explanations.
critics, Timex Group USA wants to create an interval versus H a : µ <14. Which of the following describes a
estimate for the proportion p of all consumers who Type II error?
(a)
Do these data provide convincing evidence for the
T11 The U.S. Forest Service is considering additional
(A) 10 minutes
(D) 17 minutes
Which of the following represents possible values for
believe what is shown in Timex television commercials. (A) Finding convincing evidence the bags are being
Pew Research Center’s claim?
restrictions on the number of vehicles allowed to enter
the median and IQR of waiting times for the emer-
Which of the following is the smallest number of con- underfilled when they really aren’t.
(B) 12 minutes
(E) 24 minutes
Yellowstone National Park. To assess public reaction,
(b) Which type of error, Type I or Type II, could you have
gency room last month?
sumers that Timex can survey to guarantee a margin of (B) Finding convincing evidence the bags are being
(C) 15 minutes
the service asks a random sample of 150 visitors if they
error of 0.05 or less at a 99% confidence level? underfilled when they really are. = minutes
(A) median = 27 minutes and
made in part (a)? Explain your answer. 15IQR
favor the proposal. Of these, 89 say “Yes.”
(A) 550 AP13 For an experiment comparing two treatments (A and (C) Not finding convincing evidence the bags are
(D) 700
= 25 minutes
(B) median = 28 minutes and IQR
T13 A mattress manufacturer has designed a new produc-
(a)
Construct and interpret a 99% confidence interval for
B), the experimental units are eight rats, of which four
(B) 600 the proportion of all visitors to Yellowstone who favor being underfilled when they really are. = 35 minutes
(E) 750
(C) median = 31 minutes and IQR
tion process that is intended to reduce the proportion
are female (F1, F2, F3, F4) and four are male (M1,
of mattresses with defects in the stitching. Before the
(C) 650 the restrictions. (D) Not finding convincing evidence the bags are
= 45 minutes
(D) median = 35 minutes and IQR
M2, M3, M4). If a randomized block design is used,
change, 15% of the mattresses had this type of defect.
(b) Interpret the confidence level. being underfilled when they really aren’t. = 55 minutes
with the experimental units blocked by sex, which of
(E) median = 45 minutes and IQR
After the new production process is implemented, 100
T3 A random sample of 100 likely voters in a small city (E) Finding convincing evidence the bags are being
the following is a valid assignment of treatments?
produced 59 voters in favor of Candidate A. The value overfilled when they are really underfilled.
mattresses will be randomly selected and inspected
T12 According to the Pew Research Center, “More than
AP15 A child is 40 inches tall, which places the child
(A) A: (F1, F2, M3, F4), B: (M1, F3, M2, M4)
of the standardized test statistic for performing a test of for stitching defects. Then the manufacturer will test
at the 90th percentile of all children of similar
half of Americans live within an hour of extended
H : 0 p = 0.5 versus H p > 0.5 is which of the following? T6 A 95% confidence interval for the proportion of viewers
< 0.15.
(B) A: (F2, M1, M4, M2), B: (F4, F3, M3, F1)
= 0.15 versus H p
: 0 p
H age. The heights for children of this age form an
family.” In this study, “extended family” was defined
: a
: a
approximately normal distribution with a mean of
0.59 A: (M2, F1, M3, F3), B: (M1, F4, F2, M4) of a certain reality television show who are older than age
(C)
(a)
as children, parents, grandparents, grandchildren,
The company statistician calculates that the power
−0.5
®
(A) = brothers, sisters, cousins, aunts, uncles, and in-laws, 30 is (0.26, 0.35). Suppose the show’s producers want to
z
Four CUMULATIVE AP PRACTICE
38 inches. Based on this information, what is the
of the test to detect = 0.10p
using α = 0.05 is 0.39.
(D) A: (F1, F2, F3, F4), B: (M1, M2, M3, M4)
0.59(0.41)
Cumulative AP® Practice Test 1 and “within an hour” was the amount of time it would test the hypothesis H p = 0.25 against H pof all children of
≠ 0.25.
Interpret this value.
standard deviation of the heights
: 0
: a
(E)
100 A: (M4, M1, F1, M3), B: (F4, F2, M2, F3)
Which of the following is an appropriate conclusion for
TESTS simulate the real exam. Placed
this age?
take to drive to visit the extended family. Pew’s claim
(b) After inspecting 100 randomly selected mattresses, 11
was based on a random sample of 9676 U.S. adults in
−0.5
were found to have defects in the stitching, resulting
(A) 0.20 inch
AP14
(B) = 0.59 The frequency table summarizes the distribution of them to draw at the α = 0.05 significance level?
z
after Units 3, 5, 7, and 9, these
which 55% said they lived within an hour of extended
time that 140 patients at the emergency room of a
(B) 0.31 inch
in a P-value of 0.13. Interpret this value.
0
0.5(0.5) (A) Fail to reject H ; there is convincing statistical
family. evidence that the true proportion of viewers of
small-city hospital waited to receive medical attention
(C) 0.65 inch
100
Section I: Multiple Choice Choose the best answer for each question. during the last month. tests expand in coverage of content
this reality TV show who are older than age 30
(D) 1.21 inches
0.5 −0.59 equals 0.25.
z
AP1 You look at real estate ads for houses in Sarasota, AP4 For a biology project, you measure the weight in Frequency (B) Fail to reject H ; there is not convincing statisti-
(C) =
Waiting time
(E) 1.56 inches
0.59(0.41)
0
Florida. Many houses have prices from $200,000 to grams (g) and the tail length in millimeters (mm) of a 5 and skills as you work through the
Less than 10 minutes
100
$400,000. The few houses on the water, however, group of mice. The equation of the least-squares line 24 cal evidence that the true proportion of viewers
At least 10 but less than 20 minutes
of this reality TV show who are older than age 30
have prices up to $15 million. Which of the follow- for predicting tail length from weight is book. The last test models a full
0.5
ing statements best describes the distribution of home predictedtaillength −0.59 At least 20 but less than 30 minutes 45 differs from 0.25.
®
z
(D) =
+ ×weight
AP Statistics exam.
= 20
3
prices in Sarasota? 0.5(0.5) At least 30 but less than 40 minutes 38 (C) Reject H ; there is not convincing statistical evi-
0
100 correct?
(A) The distribution is most likely skewed to the left, Which of the following is not At least 40 but less than 50 minutes 19 dence that the true proportion of viewers of this
reality TV show who are older than age 30 differs
and the mean is greater than the median. (A) A mouse’s predicted tail length increases by about 7
At least 50 but less than 60 minutes
−0.5
0.59
(E) =
At least 60 but less than 70 minutes
(B) The distribution is most likely skewed to the left, 3 mm for each additional gram of weight. 2 from 0.25.
z
100
and the mean is less than the median. (B) The predicted tail length of a mouse that weighs (D) Reject H ; there is convincing statistical evidence
0
that the true proportion of viewers of this reality TV
(C) The distribution is roughly symmetric with a few 38 g is 134 mm. Section II: Part A Show all your work. Indicate clearly the methods you use, because you will be graded on the
show who are older than age 30 is greater than 0.25.
correctness of your methods as well as on the accuracy and completeness of your results and explanations.
high outliers, and the mean is approximately (C) The correlation between weight and tail length is
T4
= 0.4 against H p
In a test of H p
≠ 0.4, a random
: 0
: a
0
equal to the median. positive. sample of size 100 yields a standardized test statistic (E) Reject H ; there is convincing statistical evi-
Write a few sentences comparing the distributions of
(a)
AP16 The manufacturer of exercise machines for fitness
(D) The distribution is most likely skewed to the right, (D) If you had measured the tail length in centime- dence that the true proportion of viewers of this
z
of = 1.28. Which of the following is closest to the
centers has designed two new elliptical machines that
reality TV show who are older than age 30 differs elliptical
cardiovascular fitness gains from the two
P-value for this test?
and the mean is greater than the median. ters instead of millimeters, the slope of the regres- from 0.25.
are meant to increase cardiovascular fitness. The two
machines.
(E) The distribution is most likely skewed to the right, sion line would have been 3/10 = 0.3. (b) Which machine should be chosen if the company
machines are being tested on 30 volunteers at a fitness
and the mean is less than the median. (E) Mice that have a weight of 0 g will have a tail of wants to advertise it as achieving the highest over-
center near the company’s headquarters. The volun-
length 20 mm. teers are randomly assigned to one of the machines
AP2 The distribution of test scores for a large statistics class and use it daily for two months. A measure of car- all gain in cardiovascular fitness? Explain your
is summarized in the boxplot. If a score of at least 70 is AP5 The weights of bananas from a certain tree are approx- reasoning.
diovascular fitness is administered at the start of the
considered passing, about what percentage of students imately normally distributed with a mean of 156 (c) Which machine should be chosen if the company
experiment and again at the end. The following stem-
in the class passed the test? grams and a standard deviation of 11 grams. Approx- wants to advertise it as achieving the most consis-
plot contains the differences (After - Before) in the
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07_StarnesTPS7e_40934_un06_529_642.indd 604
imately what proportion of bananas from this tree tent gain in cardiovascular fitness? Explain your
two scores for subjects using the two machines. Note
weigh between 150 and 160 grams? reasoning.
that greater differences indicate larger gains in fitness.
(A) 0.10 (D) 0.68 (d) What is the largest population to which we can apply
(E) 0.95
50 60 70 80 90 100 (B) 0.35 Machine A Machine B the results of this study?
Test score 0 2
(C) 0.65 54 1 0 Key: 2 | 1 represents a AP17 A national tire company wants to compare two dif -
Stra AP6 In retail stores, there is a lot of competition for shelf difference (After 2 Before) ferent types of incentives for increasing sales: award-
(B) 50tegies for Success on the
876320
2
159
of 21 in tness scores.
(A) 25
ing cash bonuses or awarding noncash prizes such as
97411
2489
3
space. To investigate the relationship between shelf
257
vacations. The company has 60 retail sales districts
61
4
5
359
AP® Statistics Exam space and sales, the amount of space allocated to a of various sizes across the country and will randomly
(C) 70
certain type of product is randomly varied between 3
and 6 linear feet over the next 12 weeks, and weekly
(D) 75
(E) Cannot be determined without the raw data. sales revenue (in dollars) for that type of product is
recorded. Here is some computer output from the
AP3 Here are the times, in seconds, to run 400 meters for study: 07_StarnesTPS7e_40934_un06_529_642.indd 606 09/10/23 1:40 PM
10 students in a physical education class: Consult the STRATEGIES FOR
ABOUT THE AP® STATISTICS EXAM Predictor Coef SE Coef T P 09/10/23 12:51 PM
04_StarnesTPS7e_40934_un03_239_316.indd 315
145 139 126 122 124 130 96 110 118 118 Constant 317.940 31.32 10.15 0.000 ®
The AP ® Statistics exam consists of two distinct sections: Multiple Choice and Free Response. 6.445 23.69 0.000 SUCCESS ON THE AP STATISTICS
Shelf length 152.680
Here are specific details about the structure and scoring of the exam, as of Fall 2023. R-Sq =98.2% R-Sq(adj)98.1
For these data, what is the lower outlier boundary

=
S22.9212
=
×
according to the 1.5 IQR rule? EXAM appendix for insight into the
®
(A) 18 (D) 105 Calculate the residual for the week where the shelf AP Statistics exam and advice on
AP® STATISTICS EXAM STRUCTURE
length was 3.5 feet and the sales were $825.
(B) 96
Section I: Multiple Choice (E) 110 90 minutes (A) −$427 50% of exam score
(D) $427
(C) 100
40 multiple choice questions, each with 5 answer choices how to take it with confidence.
(B) −$27
(E) $852
The composition of the Multiple Choice section is based on both content and skills. Here are the number of questions for each unit
and skill category. (C) $27
Unit Number of questions
Unit 1: Exploring One-Variable Data 6–9 xxv
Unit 2: Exploring Two-Variable Data 2–3 313
Unit 3: Collecting Data 5–6
Unit 4: Probability, Random Variables, and Probability Distributions 4–8
Unit 5: Sampling Distributions
3–5
© 2024 BFW Publishers PAGES NOT FINAL - For Review Purposes Only, all other uses prohibited - Do Not Copy or Post in Any Form.
5–6
Unit 6: Inference for Categorical Data: Proportions
04_StarnesTPS7e_40934_un03_239_316.indd 313 09/10/23 12:50 PM
Unit 7: Inference for Quantitative Data: Means 4–7
Unit 8: Inference for Categorical Data: Chi-Square 1–2
Unit 9: Inference for Quantitative Data: Slopes 1–2
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Skill Category Number of questions
Skill 1: Selecting Statistical Methods 6–9
Skill 2: Data Analysis 6–9
Skill 3: Using Probability and Simulation 12–16
Skill 4: Statistical Argumentation 10–14
Section II: Free Response 90 minutes 50% of exam score
Part A: Questions 1–5 65 minutes 37.5% of exam score
Part B: Question 6 (Investigative Task) 25 minutes 12.5% of exam score
The composition of the Free Response section is based on • One multi-part question focusing primarily on Probability and Sampling

skills. The first 5 free-response questions (Part A) include Distributions (Skill Category 3)
the following: • One question focusing primarily on Inference (Skill Categories 1, 3, 4)
• One multi-part question focusing primarily on Explor- • One question focusing on two or more skill categories
ing Data (Skill Category 2)
The sixth free-response question (Part B) is the Investigative Task, which
• One multi-part question focusing primarily on Collect- assesses multiple skill categories and content areas, focusing on applying
ing Data (Skill Category 1) the skills and content in new contexts or nonroutine ways.
Formulas, Tables, and Calculator Use
The Formula Sheet and Tables (Table A: Standard normal probabilities, Table B: t distribution critical values, Table C: χ 2 critical
values) are provided on both sections of the exam. Find examples in AP ® Classroom, on a recent AP ® Statistics exam (2021 or later), or
in the back of the book. The formulas are found at the beginning of the test booklets and the tables are found at the end, for both the
Multiple Choice and Free Response sections. You may use your calculator throughout the exam.
A-1
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