INSTRUCTOR ANSWER GUIDE
OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
,OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
CHAPTER 1: SAMPLING AND DATA
Exercise 1. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
A fitness center is interested in the mean amount of time a client exercises in
the center each week.
Solution a. The population is all of the clients of the fitness center.
b. A sample of the clients that use the fitness center for a given week.
c. The average amount of time that all clients exercise in one week.
d. The average amount of time that a sample of clients exercises in one week.
e. The amount of time that a client exercises in one week.
f. Examples are: 2 hours, 5 hours, and 7.5 hours
Exercise 2. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
Ski resorts are interested in the mean age that children take their first ski and
snowboard lessons. They need this information to plan their ski classes
optimally.
Solution a. all children who take ski or snowboard lessons
b. a group of these children
c. the population mean age of children who take their first snowboard lesson
d. the sample mean age of children who take their first snowboard lesson
e. X = the age of one child who takes their first ski or snowboard lesson
f. values for X, such as 3, 7, and so on
Exercise 3. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
A cardiologist is interested in the mean recovery period of her patients who
have had heart attacks.
Solution a. the cardiologist’s patients
b. a group of the cardiologist’s patients
c. the mean recovery period of all of the cardiologist’s patients
d. the mean recovery period of the group of the cardiologist’s patients
e. X = the mean recovery period of one patient
f. values for X, such as 10 days, 14 days, 20 days, and so on
Exercise 4. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
Insurance companies are interested in the mean health costs each year of
their clients, so that they can determine the costs of health insurance.
Solution a. the clients of the insurance companies
b. a group of the clients
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Chapter 1: Sampling and Data
c. the mean health costs of the clients
d. the mean health costs of the sample
e. X = the health costs of one client
f. values for X, such as 34, 9, 82, and so on
Exercise 5. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
A politician is interested in the proportion of voters in his district who think he
is doing a good job.
Solution a. all voters in the politician’s district
b. a random selection of voters in the politician’s district
c. the proportion of voters in this district who think this politician is doing a
good job
d. the proportion of voters in this district who think this politician is doing a
good job in the sample
e. X = the number of voters in the district who think this politician is doing a
good job
f. Yes, he is doing a good job. No, he is not doing a good job.
Exercise 6. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
A marriage counselor is interested in the proportion of clients she counsels
who stay married.
Solution a. all the clients of this counselor
b. a group of clients of this marriage counselor
c. the proportion of all their clients who stay married
d. the proportion of the sample of the counselor’s clients who stay married
e. X = the number of couples who stay married
f. yes, no
Exercise 7. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
Political pollsters may be interested in the proportion of people who will vote
for a particular cause.
Solution a. all voters (in a certain geographic area)
b. a random selection of all the voters
c. the proportion of voters who are interested in this particular cause
d. the proportion of voters who are interested in this particular cause in the
sample
e. X = the number of voters who are interested in this particular cause
f. yes, no
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Exercise 8. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
A marketing company is interested in the proportion of people who will buy a
particular product.
Solution a. all people (maybe in a certain geographic area, such as the United States)
b. a group of the people
c. the proportion of all people who will buy the product
d. the proportion of the sample who will buy the product
e. X = the number of people who will buy it
f. buy, not buy
Exercise 9. A Lake Tahoe Community College instructor is interested in the mean number
of days Lake Tahoe Community College math students are absent from class
during a quarter. What is the population she is interested in?
a. all Lake Tahoe Community College students
b. all Lake Tahoe Community College English students
c. all Lake Tahoe Community College students in the instructor’s classes
d. all Lake Tahoe Community College math students
Solution D
Exercise 10. A Lake Tahoe Community College instructor is interested in the mean number
of days Lake Tahoe Community College math students are absent from class
during a quarter.
Consider the following:
X = number of days a Lake Tahoe Community College math student is absent
In this case, X is an example of a:
a. variable.
b. population.
c. statistic.
d. data.
Solution A
Exercise 11. A Lake Tahoe Community College instructor is interested in the mean number
of days Lake Tahoe Community College math students are absent from class
during a quarter.
The instructor’s sample produces a mean number of days absent of 3.5 days.
This value is an example of a:
a. parameter.
b. data.
c. statistic.
d. variable.
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Chapter 1: Sampling and Data
Solution C
Exercise 12. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
number of tickets sold to a concert
Solution quantitative discrete, 150
Exercise 13. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
percent of body fat
Solution quantitative continuous, 19.2%
Exercise 14. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
favorite baseball team
Solution qualitative, Oakland A’s
Exercise 15. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
time in line to buy groceries
Solution quantitative continuous, 7.2 minutes
Exercise 16. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
number of students enrolled at Evergreen Valley College
Solution quantitative discrete, 11,234 students
Exercise 17. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
most-watched television show
Solution qualitative, Dancing with the Stars
Exercise 18. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
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example of the data.
brand of toothpaste
Solution qualitative, Crest
Exercise 19. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
distance to the closest movie theatre
Solution quantitative continuous, 8.32 miles
Exercise 20. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
age of executives in Fortune 500 companies
Solution quantitative continuous, 47.3 years
Exercise 21. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
number of competing computer spreadsheet software packages
Solution quantitative discrete, three
Exercise 22. A study was done to determine the age, number of times per week, and the
duration (amount of time) of resident use of a local park in San Jose. The first
house in the neighborhood around the park was selected randomly and then
every 8th house in the neighborhood around the park was interviewed.
“Number of times per week” is what type of data?
a. qualitative
b. quantitative discrete
c. quantitative continuous
Solution B
Exercise 23. A study was done to determine the age, number of times per week, and the
duration (amount of time) of resident use of a local park in San Jose. The first
house in the neighborhood around the park was selected randomly and then
every 8th house in the neighborhood around the park was interviewed.
“Duration (amount of time)” is what type of data?
a. qualitative
b. quantitative discrete
c. quantitative continuous
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Chapter 1: Sampling and Data
Solution C
Exercise 24. Airline companies are interested in the consistency of the number of babies on
each flight, so that they have adequate safety equipment. Suppose an airline
conducts a survey. Over Thanksgiving weekend, it surveys six flights from
Boston to Salt Lake City to determine the number of babies on the flights. It
determines the amount of safety equipment needed by the result of that study.
a. Using complete sentences, list three things wrong with the way the survey
was conducted.
b. Using complete sentences, list three ways that you would improve the
survey if it were to be repeated.
Solution a. The survey was conducted using six similar flights.
The survey would not be a true representation of the entire population of air
travelers.
Conducting the survey on a holiday weekend will not produce representative
results.
b. Conduct the survey during different times of the year.
Conduct the survey using flights to and from various locations.
Conduct the survey on different days of the week.
Exercise 25. Suppose you want to determine the mean number of students per statistics
class in your state. Describe a possible sampling method in three to five
complete sentences. Make the description detailed.
Solution Answers will vary. Sample Answer: Randomly choose 25 colleges in the
state. Use all statistics classes from each of the chosen colleges in the sample.
This can be done by listing all the colleges together with a two-digit number
starting with 00 then 01, etc. The list of colleges can be found on Wikipedia.
http://en.wikipedia.org/wiki/List_of_colleges_and_universities_in_California
Use a random number generator to pick 25 colleges.
Exercise 26. Suppose you want to determine the mean number of cans of soda drunk each
month by students in their twenties at your school. Describe a possible
sampling method in three to five complete sentences. Make the description
detailed.
Solution Answers will vary. Sample Answer: You could use a systematic sampling
method. Stop the tenth person as they leave one of the buildings on campus at
9:50 in the morning. Then stop the tenth person as they leave a different
building on campus at 1:50 in the afternoon.
Exercise 27. List some practical difficulties involved in getting accurate results from a
telephone survey.
Solution Answers will vary. Sample Answer: Not all people have a listed phone
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Instructor Answer Guide
number. Many people hang up or do not respond to phone surveys.
Exercise 28. List some practical difficulties involved in getting accurate results from a
mailed survey.
Solution Answers will vary. Sample Answer: Many people will not respond to mail
surveys. If they do respond to the surveys, you can’t be sure who is
responding. In addition, mailing lists can be incomplete.
Exercise 29. With your classmates, brainstorm some ways you could overcome these
problems if you needed to conduct a phone or mail survey.
Solution Ask everyone to include their age then take a random sample from the data.
Include in the report how the survey was conducted and why the results may
not be accurate.
Exercise 30. The instructor takes a sample by gathering data on five randomly selected
students from each Lake Tahoe Community College math class. The type of
sampling used is
a. cluster sampling
b. stratified sampling
c. simple random sampling
d. convenience sampling
Solution B
Exercise 31. A study was done to determine the age, number of times per week, and the
duration (amount of time) of residents using a local park in San Jose. The first
house in the neighborhood around the park was selected randomly and then
every eighth house in the neighborhood around the park was interviewed. The
sampling method was:
a. simple random
b. systematic
c. stratified
d. cluster
Solution b
Exercise 32. Name the sampling method used in each of the following situations:
a. A person in the airport is handing out questionnaires to travelers asking
them to evaluate the airport’s service. They do not ask travelers who are
hurrying through the airport with their hands full of luggage but instead ask
all travelers who are sitting near gates and not taking naps while they wait.
b. A teacher wants to know if students are doing homework, so they randomly
select rows two and five and then call on all students in row two and all
students in row five to present the solutions to homework problems to the
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Chapter 1: Sampling and Data
class.
c. The marketing manager for an electronics chain store wants information
about the ages of its customers. Over the next two weeks, at each store
location, 100 randomly selected customers are given questionnaires to fill out
asking for information about age, as well as about other variables of interest.
d. The librarian at a public library wants to determine what proportion of the
library users are children. The librarian has a tally sheet on which they mark
whether books are checked out by an adult or a child. The librarian records
this data for every fourth patron who checks out books.
e. A political party wants to know the reaction of voters to a debate between
the candidates. The day after the debate, the party’s polling staff calls 1,200
randomly selected phone numbers. If a registered voter answers the phone or
is available to come to the phone, that registered voter is asked whom they
intend to vote for and whether the debate changed their opinion of the
candidates.
Solution a. convenience
b. cluster
c. stratified
d. systematic
e. simple random
Exercise 33. A “random survey” was conducted of 3,274 people of the “microprocessor
generation” (people born since 1971, the year the microprocessor was
invented). It was reported that 48% of those individuals surveyed stated that if
they had $2,000 to spend, they would use it for computer equipment. Also,
66% of those surveyed considered themselves relatively savvy computer users.
a. Do you consider the sample size large enough for a study of this type? Why
or why not?
b. Based on your “gut feeling,” do you believe the percents accurately reflect
the U.S. population for those individuals born since 1971? If not, do you think
the percents of the population are actually higher or lower than the sample
statistics? Why?
Additional information: The survey, reported by Intel Corporation, was filled
out by individuals who visited the Los Angeles Convention Center to see the
Smithsonian Institute's road show called “America’s Smithsonian.”
c. With this additional information, do you feel that all demographic and
ethnic groups were equally represented at the event? Why or why not?
d. With the additional information, comment on how accurately you think the
sample statistics reflect the population parameters.
Solution a. Yes, in polling, samples that are from 1,200 to 1,500 observations are
considered large enough and good enough if the survey is random and is well
done.
b. We do not have enough information to decide if this is a random sample
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from the U.S. population.
c. No, this is a convenience sample taken from individuals who visited an
exhibition in the Angeles Convention Center. This sample is not
representative of the U.S. population.
d. It is possible that the two sample statistics, 48% and 66% are larger than the
true parameters in the population at large. In any event, no conclusion about
the population proportions can be inferred from this convenience sample.
Exercise 34. The Well-Being Index is a survey that follows trends of U.S. residents on a
regular basis. There are six areas of health and wellness covered in the
survey: Life Evaluation, Emotional Health, Physical Health, Healthy
Behavior, Work Environment, and Basic Access. Identify the type of data
obtained from each question used in this survey: qualitative, quantitative
discrete, or quantitative continuous.
a. Do you have any health problems that prevent you from doing any of the
things people your age can normally do?
b. During the past 30 days, for about how many days did poor health keep you
from doing your usual activities?
c. In the last seven days, on how many days did you exercise for 30 minutes or
more?
d. Do you have health insurance coverage?
Solution a. qualitative
b. quantitative discrete
c. quantitative discrete
d. qualitative
Exercise 35. In advance of the 1936 Presidential Election, a magazine titled Literary
Digest released the results of an opinion poll predicting that the republican
candidate Alf Landon would win by a large margin. The magazine sent post
cards to approximately 10,000,000 prospective voters. These prospective
voters were selected from the subscription list of the magazine, from
automobile registration lists, from phone lists, and from club membership
lists. Approximately 2,300,000 people returned the postcards.
a. Think about the state of the United States in 1936. Explain why a sample
chosen from magazine subscription lists, automobile registration lists, phone
books, and club membership lists was not representative of the population of
the United States at that time.
b. What effect does the low response rate have on the reliability of the
sample?
c. Are these problems examples of sampling error or nonsampling error?
d. During the same year, George Gallup conducted his own poll of 30,000
prospective voters. His researchers used a method they called "quota
sampling" to obtain survey answers from specific subsets of the population.
Quota sampling is an example of which sampling method described in this
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,OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
CHAPTER 1: SAMPLING AND DATA
Exercise 1. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
A fitness center is interested in the mean amount of time a client exercises in
the center each week.
Solution a. The population is all of the clients of the fitness center.
b. A sample of the clients that use the fitness center for a given week.
c. The average amount of time that all clients exercise in one week.
d. The average amount of time that a sample of clients exercises in one week.
e. The amount of time that a client exercises in one week.
f. Examples are: 2 hours, 5 hours, and 7.5 hours
Exercise 2. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
Ski resorts are interested in the mean age that children take their first ski and
snowboard lessons. They need this information to plan their ski classes
optimally.
Solution a. all children who take ski or snowboard lessons
b. a group of these children
c. the population mean age of children who take their first snowboard lesson
d. the sample mean age of children who take their first snowboard lesson
e. X = the age of one child who takes their first ski or snowboard lesson
f. values for X, such as 3, 7, and so on
Exercise 3. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
A cardiologist is interested in the mean recovery period of her patients who
have had heart attacks.
Solution a. the cardiologist’s patients
b. a group of the cardiologist’s patients
c. the mean recovery period of all of the cardiologist’s patients
d. the mean recovery period of the group of the cardiologist’s patients
e. X = the mean recovery period of one patient
f. values for X, such as 10 days, 14 days, 20 days, and so on
Exercise 4. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
Insurance companies are interested in the mean health costs each year of
their clients, so that they can determine the costs of health insurance.
Solution a. the clients of the insurance companies
b. a group of the clients
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Chapter 1: Sampling and Data
c. the mean health costs of the clients
d. the mean health costs of the sample
e. X = the health costs of one client
f. values for X, such as 34, 9, 82, and so on
Exercise 5. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
A politician is interested in the proportion of voters in his district who think he
is doing a good job.
Solution a. all voters in the politician’s district
b. a random selection of voters in the politician’s district
c. the proportion of voters in this district who think this politician is doing a
good job
d. the proportion of voters in this district who think this politician is doing a
good job in the sample
e. X = the number of voters in the district who think this politician is doing a
good job
f. Yes, he is doing a good job. No, he is not doing a good job.
Exercise 6. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
A marriage counselor is interested in the proportion of clients she counsels
who stay married.
Solution a. all the clients of this counselor
b. a group of clients of this marriage counselor
c. the proportion of all their clients who stay married
d. the proportion of the sample of the counselor’s clients who stay married
e. X = the number of couples who stay married
f. yes, no
Exercise 7. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
Political pollsters may be interested in the proportion of people who will vote
for a particular cause.
Solution a. all voters (in a certain geographic area)
b. a random selection of all the voters
c. the proportion of voters who are interested in this particular cause
d. the proportion of voters who are interested in this particular cause in the
sample
e. X = the number of voters who are interested in this particular cause
f. yes, no
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Exercise 8. Identify: a. the population, b. the sample, c. the parameter, d. the statistic, e.
the variable, and f. the data. Give examples where appropriate.
A marketing company is interested in the proportion of people who will buy a
particular product.
Solution a. all people (maybe in a certain geographic area, such as the United States)
b. a group of the people
c. the proportion of all people who will buy the product
d. the proportion of the sample who will buy the product
e. X = the number of people who will buy it
f. buy, not buy
Exercise 9. A Lake Tahoe Community College instructor is interested in the mean number
of days Lake Tahoe Community College math students are absent from class
during a quarter. What is the population she is interested in?
a. all Lake Tahoe Community College students
b. all Lake Tahoe Community College English students
c. all Lake Tahoe Community College students in the instructor’s classes
d. all Lake Tahoe Community College math students
Solution D
Exercise 10. A Lake Tahoe Community College instructor is interested in the mean number
of days Lake Tahoe Community College math students are absent from class
during a quarter.
Consider the following:
X = number of days a Lake Tahoe Community College math student is absent
In this case, X is an example of a:
a. variable.
b. population.
c. statistic.
d. data.
Solution A
Exercise 11. A Lake Tahoe Community College instructor is interested in the mean number
of days Lake Tahoe Community College math students are absent from class
during a quarter.
The instructor’s sample produces a mean number of days absent of 3.5 days.
This value is an example of a:
a. parameter.
b. data.
c. statistic.
d. variable.
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Chapter 1: Sampling and Data
Solution C
Exercise 12. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
number of tickets sold to a concert
Solution quantitative discrete, 150
Exercise 13. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
percent of body fat
Solution quantitative continuous, 19.2%
Exercise 14. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
favorite baseball team
Solution qualitative, Oakland A’s
Exercise 15. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
time in line to buy groceries
Solution quantitative continuous, 7.2 minutes
Exercise 16. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
number of students enrolled at Evergreen Valley College
Solution quantitative discrete, 11,234 students
Exercise 17. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
most-watched television show
Solution qualitative, Dancing with the Stars
Exercise 18. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
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example of the data.
brand of toothpaste
Solution qualitative, Crest
Exercise 19. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
distance to the closest movie theatre
Solution quantitative continuous, 8.32 miles
Exercise 20. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
age of executives in Fortune 500 companies
Solution quantitative continuous, 47.3 years
Exercise 21. Identify the type of data that would be used to describe a response
(quantitative discrete, quantitative continuous, or qualitative), and give an
example of the data.
number of competing computer spreadsheet software packages
Solution quantitative discrete, three
Exercise 22. A study was done to determine the age, number of times per week, and the
duration (amount of time) of resident use of a local park in San Jose. The first
house in the neighborhood around the park was selected randomly and then
every 8th house in the neighborhood around the park was interviewed.
“Number of times per week” is what type of data?
a. qualitative
b. quantitative discrete
c. quantitative continuous
Solution B
Exercise 23. A study was done to determine the age, number of times per week, and the
duration (amount of time) of resident use of a local park in San Jose. The first
house in the neighborhood around the park was selected randomly and then
every 8th house in the neighborhood around the park was interviewed.
“Duration (amount of time)” is what type of data?
a. qualitative
b. quantitative discrete
c. quantitative continuous
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Chapter 1: Sampling and Data
Solution C
Exercise 24. Airline companies are interested in the consistency of the number of babies on
each flight, so that they have adequate safety equipment. Suppose an airline
conducts a survey. Over Thanksgiving weekend, it surveys six flights from
Boston to Salt Lake City to determine the number of babies on the flights. It
determines the amount of safety equipment needed by the result of that study.
a. Using complete sentences, list three things wrong with the way the survey
was conducted.
b. Using complete sentences, list three ways that you would improve the
survey if it were to be repeated.
Solution a. The survey was conducted using six similar flights.
The survey would not be a true representation of the entire population of air
travelers.
Conducting the survey on a holiday weekend will not produce representative
results.
b. Conduct the survey during different times of the year.
Conduct the survey using flights to and from various locations.
Conduct the survey on different days of the week.
Exercise 25. Suppose you want to determine the mean number of students per statistics
class in your state. Describe a possible sampling method in three to five
complete sentences. Make the description detailed.
Solution Answers will vary. Sample Answer: Randomly choose 25 colleges in the
state. Use all statistics classes from each of the chosen colleges in the sample.
This can be done by listing all the colleges together with a two-digit number
starting with 00 then 01, etc. The list of colleges can be found on Wikipedia.
http://en.wikipedia.org/wiki/List_of_colleges_and_universities_in_California
Use a random number generator to pick 25 colleges.
Exercise 26. Suppose you want to determine the mean number of cans of soda drunk each
month by students in their twenties at your school. Describe a possible
sampling method in three to five complete sentences. Make the description
detailed.
Solution Answers will vary. Sample Answer: You could use a systematic sampling
method. Stop the tenth person as they leave one of the buildings on campus at
9:50 in the morning. Then stop the tenth person as they leave a different
building on campus at 1:50 in the afternoon.
Exercise 27. List some practical difficulties involved in getting accurate results from a
telephone survey.
Solution Answers will vary. Sample Answer: Not all people have a listed phone
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number. Many people hang up or do not respond to phone surveys.
Exercise 28. List some practical difficulties involved in getting accurate results from a
mailed survey.
Solution Answers will vary. Sample Answer: Many people will not respond to mail
surveys. If they do respond to the surveys, you can’t be sure who is
responding. In addition, mailing lists can be incomplete.
Exercise 29. With your classmates, brainstorm some ways you could overcome these
problems if you needed to conduct a phone or mail survey.
Solution Ask everyone to include their age then take a random sample from the data.
Include in the report how the survey was conducted and why the results may
not be accurate.
Exercise 30. The instructor takes a sample by gathering data on five randomly selected
students from each Lake Tahoe Community College math class. The type of
sampling used is
a. cluster sampling
b. stratified sampling
c. simple random sampling
d. convenience sampling
Solution B
Exercise 31. A study was done to determine the age, number of times per week, and the
duration (amount of time) of residents using a local park in San Jose. The first
house in the neighborhood around the park was selected randomly and then
every eighth house in the neighborhood around the park was interviewed. The
sampling method was:
a. simple random
b. systematic
c. stratified
d. cluster
Solution b
Exercise 32. Name the sampling method used in each of the following situations:
a. A person in the airport is handing out questionnaires to travelers asking
them to evaluate the airport’s service. They do not ask travelers who are
hurrying through the airport with their hands full of luggage but instead ask
all travelers who are sitting near gates and not taking naps while they wait.
b. A teacher wants to know if students are doing homework, so they randomly
select rows two and five and then call on all students in row two and all
students in row five to present the solutions to homework problems to the
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Chapter 1: Sampling and Data
class.
c. The marketing manager for an electronics chain store wants information
about the ages of its customers. Over the next two weeks, at each store
location, 100 randomly selected customers are given questionnaires to fill out
asking for information about age, as well as about other variables of interest.
d. The librarian at a public library wants to determine what proportion of the
library users are children. The librarian has a tally sheet on which they mark
whether books are checked out by an adult or a child. The librarian records
this data for every fourth patron who checks out books.
e. A political party wants to know the reaction of voters to a debate between
the candidates. The day after the debate, the party’s polling staff calls 1,200
randomly selected phone numbers. If a registered voter answers the phone or
is available to come to the phone, that registered voter is asked whom they
intend to vote for and whether the debate changed their opinion of the
candidates.
Solution a. convenience
b. cluster
c. stratified
d. systematic
e. simple random
Exercise 33. A “random survey” was conducted of 3,274 people of the “microprocessor
generation” (people born since 1971, the year the microprocessor was
invented). It was reported that 48% of those individuals surveyed stated that if
they had $2,000 to spend, they would use it for computer equipment. Also,
66% of those surveyed considered themselves relatively savvy computer users.
a. Do you consider the sample size large enough for a study of this type? Why
or why not?
b. Based on your “gut feeling,” do you believe the percents accurately reflect
the U.S. population for those individuals born since 1971? If not, do you think
the percents of the population are actually higher or lower than the sample
statistics? Why?
Additional information: The survey, reported by Intel Corporation, was filled
out by individuals who visited the Los Angeles Convention Center to see the
Smithsonian Institute's road show called “America’s Smithsonian.”
c. With this additional information, do you feel that all demographic and
ethnic groups were equally represented at the event? Why or why not?
d. With the additional information, comment on how accurately you think the
sample statistics reflect the population parameters.
Solution a. Yes, in polling, samples that are from 1,200 to 1,500 observations are
considered large enough and good enough if the survey is random and is well
done.
b. We do not have enough information to decide if this is a random sample
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from the U.S. population.
c. No, this is a convenience sample taken from individuals who visited an
exhibition in the Angeles Convention Center. This sample is not
representative of the U.S. population.
d. It is possible that the two sample statistics, 48% and 66% are larger than the
true parameters in the population at large. In any event, no conclusion about
the population proportions can be inferred from this convenience sample.
Exercise 34. The Well-Being Index is a survey that follows trends of U.S. residents on a
regular basis. There are six areas of health and wellness covered in the
survey: Life Evaluation, Emotional Health, Physical Health, Healthy
Behavior, Work Environment, and Basic Access. Identify the type of data
obtained from each question used in this survey: qualitative, quantitative
discrete, or quantitative continuous.
a. Do you have any health problems that prevent you from doing any of the
things people your age can normally do?
b. During the past 30 days, for about how many days did poor health keep you
from doing your usual activities?
c. In the last seven days, on how many days did you exercise for 30 minutes or
more?
d. Do you have health insurance coverage?
Solution a. qualitative
b. quantitative discrete
c. quantitative discrete
d. qualitative
Exercise 35. In advance of the 1936 Presidential Election, a magazine titled Literary
Digest released the results of an opinion poll predicting that the republican
candidate Alf Landon would win by a large margin. The magazine sent post
cards to approximately 10,000,000 prospective voters. These prospective
voters were selected from the subscription list of the magazine, from
automobile registration lists, from phone lists, and from club membership
lists. Approximately 2,300,000 people returned the postcards.
a. Think about the state of the United States in 1936. Explain why a sample
chosen from magazine subscription lists, automobile registration lists, phone
books, and club membership lists was not representative of the population of
the United States at that time.
b. What effect does the low response rate have on the reliability of the
sample?
c. Are these problems examples of sampling error or nonsampling error?
d. During the same year, George Gallup conducted his own poll of 30,000
prospective voters. His researchers used a method they called "quota
sampling" to obtain survey answers from specific subsets of the population.
Quota sampling is an example of which sampling method described in this
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