INSTRUCTOR’S SOLUTIONS
MANUAL
DIACRITECH
E LEMENTARY S TATISTICS
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P ICTURING THE W ORLD
EIGHTH EDITION
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RON LARSON
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THE PENNSYLVANIA STATE UNIVERSITY
THE BEHREND COLLEGE
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,CONTENTS
Chapter 1 Introduction to Statistics 1
Chapter 2 Descriptive Statistics 14
Chapter 3 Probability 105
Chapter 4 Discrete Probability Distributions 140
Chapter 5 Normal Probability Distributions 173
Chapter 6 Confidence Intervals 226
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Chapter 7 Hypothesis Testing with One Sample 255
Chapter 8 Hypothesis Testing with Two Samples 308
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Chapter 9 Correlation and Regression 355
Chapter 10 Chi-Square Tests and the F-Distribution 407
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Chapter 11 Nonparametric Tests 466
Chapter 6 Alternate (Online) Confidence Intervals 517
Version
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Appendix A Alternative Presentation of the Standard 546
Normal Distribution
Appendix C Normal Probability Plots 547
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Activities 548
Case Studies 557
Uses and Abuses 584
Real Statistics−Real Decisions 596
Technology 611
Copyright © 2023 Pearson Education, Inc.
,12 CHAPTER 1 Ň INTRODUCTION TO STATISTICS
CHAPTER 1 QUIZ SOLUTIONS
1. Population: Collection of grade point averages, SAT scores, and ACT scores of all high school
seniors
Sample: Collection of grade point averages, SAT scores, and ACT scores of 1622 high school seniors
from four public high schools in the northeastern United States.
2. (a) Sample statistic. The value 42% is a numerical description of a sample of U.S. adults.
(b) Population parameter. The 90% of members that approved the contract of the new president is a
numerical description of all Board of Trustees members.
(c) Sample statistic. The value 48% is a numerical description of a sample of small business owners.
3. (a) Qualitative, because debit card personal identification numbers are labels and it does not make
sense to find differences between numbers.
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(b) Quantitative, because final scores are numerical measurements.
4. (a) Ordinal, because badge numbers can be ordered and often indicate seniority of service, but no
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meaningful mathematical computation can be performed.
(b) Ratio, because horsepower of one car can be expressed as a multiple of another.
(c) Ordinal, because data can be arranged in order, but the differences between data entries make no
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sense.
(d) Interval, because meaningful differences between years can be calculated, but a zero entry is not
an inherent zero.
5. (a) Observational study. The study does not attempt to influence the responses of the subjects and
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there is no treatment.
(b) Experiment. The study applies a treatment (video involving smoking) to the subjects.
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6. Randomized block design
7. (a) Convenience sampling is used because all the people sampled are in one convenient location.
(b) Systematic sampling is used because every tenth machine part is sampled.
(c) Stratified sampling is used because the population is first stratified and then a sample is collected
from each stratum.
8. Convenience sampling. People at campgrounds may be strongly against air pollution because they are
at an outdoor location.
Copyright © 2023 Pearson Education, Inc.
, CHAPTER 1 Ň INTRODUCTION TO STATISTICS 13
CHAPTER 1 TEST SOLUTIONS
1. (a) Sampling, because the population of New Jersey is too large for the most popular type of
investment to be easily recorded. Random sampling would be advised because it would be easy to
select people from New Jersey randomly and then record their most popular type of investment.
(b) Census, because the population is small and it is relatively easy to obtain the ages of the 30
employees.
2. (a) Sample statistic. The value of 27% is a numerical description of a sample of U.S. adults owning a
smart watch or fitness tracker.
(b) Population parameter. The average evidence-based reading and writing score of 528 is a
numerical description of all test takers in a recent year.
3. (a) Stratified sampling is used because the high school students are divided into strata (male and
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female), and a sample is selected from each stratum.
(b) Simple random sampling is used because each customer has an equal chance of being contacted,
and all samples of 625 customers have an equal chance of being selected.
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(c) Convenience sampling is used because a sample is taken from members of a population that are
readily available. The sample may be biased because the teachers at that school may not be
representative of the population of teachers.
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4. (a) Quantitative. Ratio. The number of employees are numerical measurements. A ratio of two data
values can be formed, so it makes sense to say that 40 employees are twice as many as 20
employees.
(b) Quantitative. Interval. The grade point averages (GPAs) are numerical measurements. Data can
be ordered and meaningful differences can be calculated, but it does not make sense to say that a
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person with a 3.8 GPA is twice as smart as a person with a 1.9 GPA.
5. (a) The survey question is unbiased.
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(b) The question is biased because it already suggests that the town’s ban on skateboarding in parks
is unfair. The question could be written as “What are your thoughts on the town’s ban on
skateboarding in parks?”
6. (a) Population: Collection of the responses of all U.S. physicians
Sample: Collection of the 17,461 U.S. physicians who were sampled.
(b) Both. Gender, location, employment status, specialty, and if they would choose medicine again
are qualitative because they are attributes. Age, income, and time spent seeing patients per week
are quantitative because they are numerical measurements.
(c) Nominal: gender, location, employment status, specialty, would they choose medicine again
Ratio: age, income, time spent seeing patients per week
(d) Observational study. The study does not attempt to influence the responses of the physicians and
there is no treatment.
Copyright © 2023 Pearson Education, Inc.
MANUAL
DIACRITECH
E LEMENTARY S TATISTICS
St
P ICTURING THE W ORLD
EIGHTH EDITION
ud
ym
RON LARSON
at
THE PENNSYLVANIA STATE UNIVERSITY
THE BEHREND COLLEGE
rix
,CONTENTS
Chapter 1 Introduction to Statistics 1
Chapter 2 Descriptive Statistics 14
Chapter 3 Probability 105
Chapter 4 Discrete Probability Distributions 140
Chapter 5 Normal Probability Distributions 173
Chapter 6 Confidence Intervals 226
St
Chapter 7 Hypothesis Testing with One Sample 255
Chapter 8 Hypothesis Testing with Two Samples 308
ud
Chapter 9 Correlation and Regression 355
Chapter 10 Chi-Square Tests and the F-Distribution 407
ym
Chapter 11 Nonparametric Tests 466
Chapter 6 Alternate (Online) Confidence Intervals 517
Version
at
Appendix A Alternative Presentation of the Standard 546
Normal Distribution
Appendix C Normal Probability Plots 547
rix
Activities 548
Case Studies 557
Uses and Abuses 584
Real Statistics−Real Decisions 596
Technology 611
Copyright © 2023 Pearson Education, Inc.
,12 CHAPTER 1 Ň INTRODUCTION TO STATISTICS
CHAPTER 1 QUIZ SOLUTIONS
1. Population: Collection of grade point averages, SAT scores, and ACT scores of all high school
seniors
Sample: Collection of grade point averages, SAT scores, and ACT scores of 1622 high school seniors
from four public high schools in the northeastern United States.
2. (a) Sample statistic. The value 42% is a numerical description of a sample of U.S. adults.
(b) Population parameter. The 90% of members that approved the contract of the new president is a
numerical description of all Board of Trustees members.
(c) Sample statistic. The value 48% is a numerical description of a sample of small business owners.
3. (a) Qualitative, because debit card personal identification numbers are labels and it does not make
sense to find differences between numbers.
St
(b) Quantitative, because final scores are numerical measurements.
4. (a) Ordinal, because badge numbers can be ordered and often indicate seniority of service, but no
ud
meaningful mathematical computation can be performed.
(b) Ratio, because horsepower of one car can be expressed as a multiple of another.
(c) Ordinal, because data can be arranged in order, but the differences between data entries make no
ym
sense.
(d) Interval, because meaningful differences between years can be calculated, but a zero entry is not
an inherent zero.
5. (a) Observational study. The study does not attempt to influence the responses of the subjects and
at
there is no treatment.
(b) Experiment. The study applies a treatment (video involving smoking) to the subjects.
rix
6. Randomized block design
7. (a) Convenience sampling is used because all the people sampled are in one convenient location.
(b) Systematic sampling is used because every tenth machine part is sampled.
(c) Stratified sampling is used because the population is first stratified and then a sample is collected
from each stratum.
8. Convenience sampling. People at campgrounds may be strongly against air pollution because they are
at an outdoor location.
Copyright © 2023 Pearson Education, Inc.
, CHAPTER 1 Ň INTRODUCTION TO STATISTICS 13
CHAPTER 1 TEST SOLUTIONS
1. (a) Sampling, because the population of New Jersey is too large for the most popular type of
investment to be easily recorded. Random sampling would be advised because it would be easy to
select people from New Jersey randomly and then record their most popular type of investment.
(b) Census, because the population is small and it is relatively easy to obtain the ages of the 30
employees.
2. (a) Sample statistic. The value of 27% is a numerical description of a sample of U.S. adults owning a
smart watch or fitness tracker.
(b) Population parameter. The average evidence-based reading and writing score of 528 is a
numerical description of all test takers in a recent year.
3. (a) Stratified sampling is used because the high school students are divided into strata (male and
St
female), and a sample is selected from each stratum.
(b) Simple random sampling is used because each customer has an equal chance of being contacted,
and all samples of 625 customers have an equal chance of being selected.
ud
(c) Convenience sampling is used because a sample is taken from members of a population that are
readily available. The sample may be biased because the teachers at that school may not be
representative of the population of teachers.
ym
4. (a) Quantitative. Ratio. The number of employees are numerical measurements. A ratio of two data
values can be formed, so it makes sense to say that 40 employees are twice as many as 20
employees.
(b) Quantitative. Interval. The grade point averages (GPAs) are numerical measurements. Data can
be ordered and meaningful differences can be calculated, but it does not make sense to say that a
at
person with a 3.8 GPA is twice as smart as a person with a 1.9 GPA.
5. (a) The survey question is unbiased.
rix
(b) The question is biased because it already suggests that the town’s ban on skateboarding in parks
is unfair. The question could be written as “What are your thoughts on the town’s ban on
skateboarding in parks?”
6. (a) Population: Collection of the responses of all U.S. physicians
Sample: Collection of the 17,461 U.S. physicians who were sampled.
(b) Both. Gender, location, employment status, specialty, and if they would choose medicine again
are qualitative because they are attributes. Age, income, and time spent seeing patients per week
are quantitative because they are numerical measurements.
(c) Nominal: gender, location, employment status, specialty, would they choose medicine again
Ratio: age, income, time spent seeing patients per week
(d) Observational study. The study does not attempt to influence the responses of the physicians and
there is no treatment.
Copyright © 2023 Pearson Education, Inc.
