Solution and Answer Guide: Peck, Introduction to Statistics and Data Analysis, 7e, 9798214000008;
Chapter 1: The Role of Statistics and the Data Analysis Process
Solution and Answer Guide
PECK, INTRODUCTION TO STATISTICS AND DATA ANALYSIS, 7E, 9798214000008;
CHAPTER 1: THE ROLE OF STATISTICS AND THE DATA ANALYSIS PROCESS
TABLE OF CONTENTS
End of Section Exercise Solutions .......................................................................................1
END OF SECTION EXERCISE SOLUTIONS
1. Give brief definitions of the terms descriptive statistics and inferential statistics.
Solution:
Descriptive statistics is the branch of statistics that involves the organization and
summary of the values in a data set. Inferential statistics is the branch of statistics
concerned with reaching conclusions about a population based on the information
provided by a sample.
2. Give brief definitions of the terms population and sample.
Solution:
The population is the entire collection of individuals or objects about which
information is required. A sample is a subset of the population selected for study in
some prescribed manner.
3. The National Highway Traffic Safety Administration (crashstats.nhtsa.dot.gov)
reported that in 2018, 857 cyclists were killed on public roadways in the United States
and that the average age of the cyclists killed was 47 years. These figures were based
on an analysis of the records of all traffic related deaths of cyclists on U.S. public
roadways in 2018.
a. Does the group of 857 cycling fatalities represent a census or a sample of the
cycling fatalities in 2018?
b. If the population of interest is cycling fatalities in 2018, is the given average age of
47 years a population value or was it calculated from a sample?
Solution:
a. The group of 857 bicycle fatalities represents a census of the 2018 bicycle
fatalities.
b. Because the group of 857 represents a census, the average age of 47 years is a
population value.
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
, Solution and Answer Guide: Peck, Introduction to Statistics and Data Analysis, 7e, 9798214000008;
Chapter 1: The Role of Statistics and the Data Analysis Process
4. “San Fernando Valley residents OK with 1-cent transit tax, MTA poll says” is the
headline of an article that appeared in the LA Daily News (April 12, 2016). This headline
was based on responses from a sample of 100 San Fernando Valley residents. Describe
the sample and the population of interest for this study.
Solution:
The sample is the 100 San Fernando Valley residents, and the population of interest is
all San Fernando Valley residents.
5. The student senate at a university with 15,000 students is interested in the proportion
of students who favor a change in the grading system to allow for plus and minus
grades (for example, B+, B, B–, rather than just B). Two hundred students are
interviewed to determine their attitude toward this proposed change.
a. What is the population of interest?
b. What group of students constitutes the sample in this problem?
Solution:
a. The population of interest is the set of all 15,000 students at the university.
b. The sample is the 200 students who are interviewed.
6. Data from a survey of 10,413 students and 588 teachers conducted for the Knight
Foundation were used to calculate the following estimates: 65% of students and 40%
of teachers chose freedom of speech as the most important of the rights guaranteed
by the First Amendment (USA TODAY, October 3, 2014). Are the percentages given
calculated using data from a sample of for the entire population?
Solution:
The percentages given were computed from sample data obtained by a survey.
7. The supervisors of a rural county are interested in the proportion of property owners
who support the construction of a sewer system. Because it is too costly to contact all
7,000 property owners, a survey of 500 owners is undertaken. Describe the population
and sample for this problem.
Solution:
The population is the set of all 7,000 property owners. The sample is the 500 owners
included in the survey.
8. A consumer group conducts crash tests of new model cars. To determine the severity
of damage to 2023 Toyota Camrys resulting from a 10-mph crash into a concrete wall,
the research group tests six cars of this type and assesses the amount of damage.
Describe the population and the sample for this problem.
Solution:
The population is the set of all 2019 Toyota Camrys. The sample is the set of six cars
that are tested.
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 2
accessible website, in whole or in part.
, Solution and Answer Guide: Peck, Introduction to Statistics and Data Analysis, 7e, 9798214000008;
Chapter 1: The Role of Statistics and the Data Analysis Process
9. A building contractor has a chance to buy an odd lot of 5,000 used bricks at an
auction. They are interested in determining the proportion of bricks in the lot that are
cracked and therefore unusable for their current project, but they do not have enough
time to inspect all 5,000 bricks. Instead, they check 100 bricks to determine which
ones are cracked. Describe the population and the sample for this problem.
Solution:
The population is the set of 5000 used bricks. The sample is the set of 100 bricks she
checks.
10. The authors of the article “Can Artificial Intelligence Pass the Fellowship of the Royal
College of Radiologists Examination?” (British Medical Journal [2022]: e072826)
wondered if an artificial intelligence (AI) program designed to interpret radiographs
(medical images such as X-rays and MRI scans) was as accurate as trained radiologists.
To investigate, they created 10 mock exams that were similar to the ones that
radiologists in England are required to pass before they can practice independently.
They found that the AI program passed only two of the 10 exams and was unable to
interpret a number of the images on the exams.
a. What were the researchers trying to learn? What questions motivated their
research?
b. Do you think that the study was conducted in a reasonable way? What additional
information would you want in order to evaluate this study?
Solution:
a. The researchers wanted to know if an AI program was as accurate as trained
radiologists in interpreting radiographs. The questions that motivated their
research could include a desire to interpret radiographs quickly and accurately to
speed up the onset of any necessary treatment.
b. Given that the purpose of the study was to evaluate a particular AI program, no
comparison group is needed. One potential issue has to do with sample size, and
perhaps a larger sample of mock exams would be beneficial. Overall, the study
seems to have been conducted in a reasonable way. Regarding additional
information, I would want to know if the mock exams were in fact representative
of the real exams and how were these mock exams created.
11. In a study to investigate the effect of blue light exposure on the quality and ripeness
of mangoes, researchers placed a sample of mangoes under blue light for nine days
and placed another sample of mangoes in darkness for nine days (“Blue Light
Simultaneously Induces Peel Anthocyanin Biosynthesis and Flesh Carotenoid/Sucrose
Biosynthesis in Mango Fruit,” Journal of Agricultural and Food Chemistry [2022]:
16,021 – 16,035). At the end of the nine days, they measured ripeness and sugar level
of the mangoes. Based on the data from the study, the researchers concluded that the
mangoes exposed to blue light were riper and sweeter than the mangoes that were
kept in the dark.
a. What were the researchers trying to learn? What questions motivated their
research?
b. Do you think that the study was conducted in a reasonable way? What additional
information would you want in order to evaluate this study?
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
, Solution and Answer Guide: Peck, Introduction to Statistics and Data Analysis, 7e, 9798214000008;
Chapter 1: The Role of Statistics and the Data Analysis Process
Solution:
a. The researchers were trying to learn about the effect of blue light exposure on the
quality and ripeness of mangoes. The questions that motivated their research
could include wanting to be able to sell better quality and speed up the ripening
process of mangoes.
b. The study was conducted in a reasonable way because the mangoes that were
exposed to blue light were compared to mangoes that were kept in the dark. This
way, one can be confident that differences can be attributed the presence or
absence of blue light. I would want to know if the mangoes in the two groups were
kept at the same temperature and were picked at the same time.
12. Classify each of the following variables as either categorical or numerical. For those
that are numerical, determine whether they are discrete or continuous.
a. Number of students in a class of 35 who turn in a term paper before the due date
b. Assigned Sex of the next baby born at a particular hospital
c. Amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda
pop
d. Thickness of the gelatin coating of a vitamin E capsule
e. Birth order classification (only child, firstborn, middle child, lastborn) of a math
major
Solution:
a. Numerical (discrete)
b. Categorical
c. Numerical (continuous)
d. Numerical (continuous)
e. Categorical
13. Classify each of the following variables as either categorical or numerical. For those
that are numerical, determine whether they are discrete or continuous.
a. Brand of computer purchased by a customer
b. State of birth for someone born in the United States
c. Price of a textbook
d. Concentration of a contaminant (micrograms per cubic centimeter) in a water
sample
e. Zip code (Think carefully about this one.)
f. Actual weight of coffee in a can labeled as containing 1 pound
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
Chapter 1: The Role of Statistics and the Data Analysis Process
Solution and Answer Guide
PECK, INTRODUCTION TO STATISTICS AND DATA ANALYSIS, 7E, 9798214000008;
CHAPTER 1: THE ROLE OF STATISTICS AND THE DATA ANALYSIS PROCESS
TABLE OF CONTENTS
End of Section Exercise Solutions .......................................................................................1
END OF SECTION EXERCISE SOLUTIONS
1. Give brief definitions of the terms descriptive statistics and inferential statistics.
Solution:
Descriptive statistics is the branch of statistics that involves the organization and
summary of the values in a data set. Inferential statistics is the branch of statistics
concerned with reaching conclusions about a population based on the information
provided by a sample.
2. Give brief definitions of the terms population and sample.
Solution:
The population is the entire collection of individuals or objects about which
information is required. A sample is a subset of the population selected for study in
some prescribed manner.
3. The National Highway Traffic Safety Administration (crashstats.nhtsa.dot.gov)
reported that in 2018, 857 cyclists were killed on public roadways in the United States
and that the average age of the cyclists killed was 47 years. These figures were based
on an analysis of the records of all traffic related deaths of cyclists on U.S. public
roadways in 2018.
a. Does the group of 857 cycling fatalities represent a census or a sample of the
cycling fatalities in 2018?
b. If the population of interest is cycling fatalities in 2018, is the given average age of
47 years a population value or was it calculated from a sample?
Solution:
a. The group of 857 bicycle fatalities represents a census of the 2018 bicycle
fatalities.
b. Because the group of 857 represents a census, the average age of 47 years is a
population value.
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
, Solution and Answer Guide: Peck, Introduction to Statistics and Data Analysis, 7e, 9798214000008;
Chapter 1: The Role of Statistics and the Data Analysis Process
4. “San Fernando Valley residents OK with 1-cent transit tax, MTA poll says” is the
headline of an article that appeared in the LA Daily News (April 12, 2016). This headline
was based on responses from a sample of 100 San Fernando Valley residents. Describe
the sample and the population of interest for this study.
Solution:
The sample is the 100 San Fernando Valley residents, and the population of interest is
all San Fernando Valley residents.
5. The student senate at a university with 15,000 students is interested in the proportion
of students who favor a change in the grading system to allow for plus and minus
grades (for example, B+, B, B–, rather than just B). Two hundred students are
interviewed to determine their attitude toward this proposed change.
a. What is the population of interest?
b. What group of students constitutes the sample in this problem?
Solution:
a. The population of interest is the set of all 15,000 students at the university.
b. The sample is the 200 students who are interviewed.
6. Data from a survey of 10,413 students and 588 teachers conducted for the Knight
Foundation were used to calculate the following estimates: 65% of students and 40%
of teachers chose freedom of speech as the most important of the rights guaranteed
by the First Amendment (USA TODAY, October 3, 2014). Are the percentages given
calculated using data from a sample of for the entire population?
Solution:
The percentages given were computed from sample data obtained by a survey.
7. The supervisors of a rural county are interested in the proportion of property owners
who support the construction of a sewer system. Because it is too costly to contact all
7,000 property owners, a survey of 500 owners is undertaken. Describe the population
and sample for this problem.
Solution:
The population is the set of all 7,000 property owners. The sample is the 500 owners
included in the survey.
8. A consumer group conducts crash tests of new model cars. To determine the severity
of damage to 2023 Toyota Camrys resulting from a 10-mph crash into a concrete wall,
the research group tests six cars of this type and assesses the amount of damage.
Describe the population and the sample for this problem.
Solution:
The population is the set of all 2019 Toyota Camrys. The sample is the set of six cars
that are tested.
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 2
accessible website, in whole or in part.
, Solution and Answer Guide: Peck, Introduction to Statistics and Data Analysis, 7e, 9798214000008;
Chapter 1: The Role of Statistics and the Data Analysis Process
9. A building contractor has a chance to buy an odd lot of 5,000 used bricks at an
auction. They are interested in determining the proportion of bricks in the lot that are
cracked and therefore unusable for their current project, but they do not have enough
time to inspect all 5,000 bricks. Instead, they check 100 bricks to determine which
ones are cracked. Describe the population and the sample for this problem.
Solution:
The population is the set of 5000 used bricks. The sample is the set of 100 bricks she
checks.
10. The authors of the article “Can Artificial Intelligence Pass the Fellowship of the Royal
College of Radiologists Examination?” (British Medical Journal [2022]: e072826)
wondered if an artificial intelligence (AI) program designed to interpret radiographs
(medical images such as X-rays and MRI scans) was as accurate as trained radiologists.
To investigate, they created 10 mock exams that were similar to the ones that
radiologists in England are required to pass before they can practice independently.
They found that the AI program passed only two of the 10 exams and was unable to
interpret a number of the images on the exams.
a. What were the researchers trying to learn? What questions motivated their
research?
b. Do you think that the study was conducted in a reasonable way? What additional
information would you want in order to evaluate this study?
Solution:
a. The researchers wanted to know if an AI program was as accurate as trained
radiologists in interpreting radiographs. The questions that motivated their
research could include a desire to interpret radiographs quickly and accurately to
speed up the onset of any necessary treatment.
b. Given that the purpose of the study was to evaluate a particular AI program, no
comparison group is needed. One potential issue has to do with sample size, and
perhaps a larger sample of mock exams would be beneficial. Overall, the study
seems to have been conducted in a reasonable way. Regarding additional
information, I would want to know if the mock exams were in fact representative
of the real exams and how were these mock exams created.
11. In a study to investigate the effect of blue light exposure on the quality and ripeness
of mangoes, researchers placed a sample of mangoes under blue light for nine days
and placed another sample of mangoes in darkness for nine days (“Blue Light
Simultaneously Induces Peel Anthocyanin Biosynthesis and Flesh Carotenoid/Sucrose
Biosynthesis in Mango Fruit,” Journal of Agricultural and Food Chemistry [2022]:
16,021 – 16,035). At the end of the nine days, they measured ripeness and sugar level
of the mangoes. Based on the data from the study, the researchers concluded that the
mangoes exposed to blue light were riper and sweeter than the mangoes that were
kept in the dark.
a. What were the researchers trying to learn? What questions motivated their
research?
b. Do you think that the study was conducted in a reasonable way? What additional
information would you want in order to evaluate this study?
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
, Solution and Answer Guide: Peck, Introduction to Statistics and Data Analysis, 7e, 9798214000008;
Chapter 1: The Role of Statistics and the Data Analysis Process
Solution:
a. The researchers were trying to learn about the effect of blue light exposure on the
quality and ripeness of mangoes. The questions that motivated their research
could include wanting to be able to sell better quality and speed up the ripening
process of mangoes.
b. The study was conducted in a reasonable way because the mangoes that were
exposed to blue light were compared to mangoes that were kept in the dark. This
way, one can be confident that differences can be attributed the presence or
absence of blue light. I would want to know if the mangoes in the two groups were
kept at the same temperature and were picked at the same time.
12. Classify each of the following variables as either categorical or numerical. For those
that are numerical, determine whether they are discrete or continuous.
a. Number of students in a class of 35 who turn in a term paper before the due date
b. Assigned Sex of the next baby born at a particular hospital
c. Amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda
pop
d. Thickness of the gelatin coating of a vitamin E capsule
e. Birth order classification (only child, firstborn, middle child, lastborn) of a math
major
Solution:
a. Numerical (discrete)
b. Categorical
c. Numerical (continuous)
d. Numerical (continuous)
e. Categorical
13. Classify each of the following variables as either categorical or numerical. For those
that are numerical, determine whether they are discrete or continuous.
a. Brand of computer purchased by a customer
b. State of birth for someone born in the United States
c. Price of a textbook
d. Concentration of a contaminant (micrograms per cubic centimeter) in a water
sample
e. Zip code (Think carefully about this one.)
f. Actual weight of coffee in a can labeled as containing 1 pound
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
