Solution Manual for Fundamentals of Statistics, 5th Edition
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SOLUTIONS MANUAL
GEX PUBLISHING SERVICES
F UNDAMENTALS OF S TATISTICS :
I NFORMED D ECISIONS U SING D ATA
F IFTH EDITION
Michael Sullivan, III
Joliet Junior College
GEX PUBLISHING SERVICES
F UNDAMENTALS OF S TATISTICS :
I NFORMED D ECISIONS U SING D ATA
F IFTH EDITION
Michael Sullivan, III
Joliet Junior College
Table of Contents
Preface
Chapter 1 Data Collection
1.1 Introduction to the Practice of Statistics .............................................................................................................1
1.2 Observational Studies versus Designed Experiments .........................................................................................3
1.3 Simple Random Sampling ..................................................................................................................................6
1.4 Other Effective Sampling Methods.....................................................................................................................8
1.5 Bias in Sampling ...............................................................................................................................................10
1.6 The Design of Experiments ..............................................................................................................................13
Chapter 1 Review Exercises ........................................................................................................................................19
Chapter 1 Test..............................................................................................................................................................22
Chapter 2 Summarizing Data in Tables and Graphs
2.1 Organizing Qualitative Data .............................................................................................................................25
2.2 Organizing Quantitative Data ...........................................................................................................................33
2.3 Graphical Misrepresentations of Data...............................................................................................................47
Chapter 2 Review Exercises ........................................................................................................................................49
Chapter 2 Test..............................................................................................................................................................54
Chapter 3 Numerically Summarizing Data
3.1 Measures of Central Tendency .........................................................................................................................57
3.2 Measures of Dispersion.....................................................................................................................................64
3.3 Measures of Central Tendency and Dispersion from Grouped Data ................................................................80
3.4 Measures of Position and Outliers ....................................................................................................................89
3.5 The Five-Number Summary and Boxplots .......................................................................................................97
Chapter 3 Review Exercises ......................................................................................................................................106
Chapter 3 Test............................................................................................................................................................111
Chapter 4 Describing the Relation between Two Variables
4.1 Scatter Diagrams and Correlation ...................................................................................................................116
4.2 Least-Squares Regression ...............................................................................................................................133
4.3 The Coefficient of Determination ...................................................................................................................144
4.4 Contingency Tables and Association ..............................................................................................................148
Chapter 4 Review Exercises ......................................................................................................................................155
Chapter 4 Test............................................................................................................................................................160
Chapter 5 Probability
5.1 Probability Rules.............................................................................................................................................164
5.2 The Addition Rule and Complements.............................................................................................................170
5.3 Independence and the Multiplication Rule .....................................................................................................177
5.4 Conditional Probability and the General Multiplication Rule.........................................................................181
5.5 Counting Techniques ......................................................................................................................................187
5.6 Putting It Together: Which Method Do I Use? ...............................................................................................192
Chapter 5 Review Exercises ......................................................................................................................................194
Chapter 5 Test............................................................................................................................................................197
Preface
Chapter 1 Data Collection
1.1 Introduction to the Practice of Statistics .............................................................................................................1
1.2 Observational Studies versus Designed Experiments .........................................................................................3
1.3 Simple Random Sampling ..................................................................................................................................6
1.4 Other Effective Sampling Methods.....................................................................................................................8
1.5 Bias in Sampling ...............................................................................................................................................10
1.6 The Design of Experiments ..............................................................................................................................13
Chapter 1 Review Exercises ........................................................................................................................................19
Chapter 1 Test..............................................................................................................................................................22
Chapter 2 Summarizing Data in Tables and Graphs
2.1 Organizing Qualitative Data .............................................................................................................................25
2.2 Organizing Quantitative Data ...........................................................................................................................33
2.3 Graphical Misrepresentations of Data...............................................................................................................47
Chapter 2 Review Exercises ........................................................................................................................................49
Chapter 2 Test..............................................................................................................................................................54
Chapter 3 Numerically Summarizing Data
3.1 Measures of Central Tendency .........................................................................................................................57
3.2 Measures of Dispersion.....................................................................................................................................64
3.3 Measures of Central Tendency and Dispersion from Grouped Data ................................................................80
3.4 Measures of Position and Outliers ....................................................................................................................89
3.5 The Five-Number Summary and Boxplots .......................................................................................................97
Chapter 3 Review Exercises ......................................................................................................................................106
Chapter 3 Test............................................................................................................................................................111
Chapter 4 Describing the Relation between Two Variables
4.1 Scatter Diagrams and Correlation ...................................................................................................................116
4.2 Least-Squares Regression ...............................................................................................................................133
4.3 The Coefficient of Determination ...................................................................................................................144
4.4 Contingency Tables and Association ..............................................................................................................148
Chapter 4 Review Exercises ......................................................................................................................................155
Chapter 4 Test............................................................................................................................................................160
Chapter 5 Probability
5.1 Probability Rules.............................................................................................................................................164
5.2 The Addition Rule and Complements.............................................................................................................170
5.3 Independence and the Multiplication Rule .....................................................................................................177
5.4 Conditional Probability and the General Multiplication Rule.........................................................................181
5.5 Counting Techniques ......................................................................................................................................187
5.6 Putting It Together: Which Method Do I Use? ...............................................................................................192
Chapter 5 Review Exercises ......................................................................................................................................194
Chapter 5 Test............................................................................................................................................................197
Table of Contents
Preface
Chapter 1 Data Collection
1.1 Introduction to the Practice of Statistics .............................................................................................................1
1.2 Observational Studies versus Designed Experiments .........................................................................................3
1.3 Simple Random Sampling ..................................................................................................................................6
1.4 Other Effective Sampling Methods.....................................................................................................................8
1.5 Bias in Sampling ...............................................................................................................................................10
1.6 The Design of Experiments ..............................................................................................................................13
Chapter 1 Review Exercises ........................................................................................................................................19
Chapter 1 Test..............................................................................................................................................................22
Chapter 2 Summarizing Data in Tables and Graphs
2.1 Organizing Qualitative Data .............................................................................................................................25
2.2 Organizing Quantitative Data ...........................................................................................................................33
2.3 Graphical Misrepresentations of Data...............................................................................................................47
Chapter 2 Review Exercises ........................................................................................................................................49
Chapter 2 Test..............................................................................................................................................................54
Chapter 3 Numerically Summarizing Data
3.1 Measures of Central Tendency .........................................................................................................................57
3.2 Measures of Dispersion.....................................................................................................................................64
3.3 Measures of Central Tendency and Dispersion from Grouped Data ................................................................80
3.4 Measures of Position and Outliers ....................................................................................................................89
3.5 The Five-Number Summary and Boxplots .......................................................................................................97
Chapter 3 Review Exercises ......................................................................................................................................106
Chapter 3 Test............................................................................................................................................................111
Chapter 4 Describing the Relation between Two Variables
4.1 Scatter Diagrams and Correlation ...................................................................................................................116
4.2 Least-Squares Regression ...............................................................................................................................133
4.3 The Coefficient of Determination ...................................................................................................................144
4.4 Contingency Tables and Association ..............................................................................................................148
Chapter 4 Review Exercises ......................................................................................................................................155
Chapter 4 Test............................................................................................................................................................160
Chapter 5 Probability
5.1 Probability Rules.............................................................................................................................................164
5.2 The Addition Rule and Complements.............................................................................................................170
5.3 Independence and the Multiplication Rule .....................................................................................................177
5.4 Conditional Probability and the General Multiplication Rule.........................................................................181
5.5 Counting Techniques ......................................................................................................................................187
5.6 Putting It Together: Which Method Do I Use? ...............................................................................................192
Chapter 5 Review Exercises ......................................................................................................................................194
Chapter 5 Test............................................................................................................................................................197
Preface
Chapter 1 Data Collection
1.1 Introduction to the Practice of Statistics .............................................................................................................1
1.2 Observational Studies versus Designed Experiments .........................................................................................3
1.3 Simple Random Sampling ..................................................................................................................................6
1.4 Other Effective Sampling Methods.....................................................................................................................8
1.5 Bias in Sampling ...............................................................................................................................................10
1.6 The Design of Experiments ..............................................................................................................................13
Chapter 1 Review Exercises ........................................................................................................................................19
Chapter 1 Test..............................................................................................................................................................22
Chapter 2 Summarizing Data in Tables and Graphs
2.1 Organizing Qualitative Data .............................................................................................................................25
2.2 Organizing Quantitative Data ...........................................................................................................................33
2.3 Graphical Misrepresentations of Data...............................................................................................................47
Chapter 2 Review Exercises ........................................................................................................................................49
Chapter 2 Test..............................................................................................................................................................54
Chapter 3 Numerically Summarizing Data
3.1 Measures of Central Tendency .........................................................................................................................57
3.2 Measures of Dispersion.....................................................................................................................................64
3.3 Measures of Central Tendency and Dispersion from Grouped Data ................................................................80
3.4 Measures of Position and Outliers ....................................................................................................................89
3.5 The Five-Number Summary and Boxplots .......................................................................................................97
Chapter 3 Review Exercises ......................................................................................................................................106
Chapter 3 Test............................................................................................................................................................111
Chapter 4 Describing the Relation between Two Variables
4.1 Scatter Diagrams and Correlation ...................................................................................................................116
4.2 Least-Squares Regression ...............................................................................................................................133
4.3 The Coefficient of Determination ...................................................................................................................144
4.4 Contingency Tables and Association ..............................................................................................................148
Chapter 4 Review Exercises ......................................................................................................................................155
Chapter 4 Test............................................................................................................................................................160
Chapter 5 Probability
5.1 Probability Rules.............................................................................................................................................164
5.2 The Addition Rule and Complements.............................................................................................................170
5.3 Independence and the Multiplication Rule .....................................................................................................177
5.4 Conditional Probability and the General Multiplication Rule.........................................................................181
5.5 Counting Techniques ......................................................................................................................................187
5.6 Putting It Together: Which Method Do I Use? ...............................................................................................192
Chapter 5 Review Exercises ......................................................................................................................................194
Chapter 5 Test............................................................................................................................................................197
Chapter 6 Discrete Probability Distributions
6.1 Discrete Random Variables.............................................................................................................................200
6.2 The Binomial Probability Distribution............................................................................................................208
Chapter 6 Review Exercises ......................................................................................................................................222
Chapter 6 Test............................................................................................................................................................225
Chapter 7 The Normal Probability Distribution
7.1 Properties of the Normal Distribution .............................................................................................................228
7.2 Applications of the Normal Distribution.........................................................................................................231
7.3 Assessing Normality .......................................................................................................................................250
7.4 The Normal Approximation to the Binomial Probability Distribution ...........................................................253
Chapter 7 Review Exercises ......................................................................................................................................257
Chapter 7 Test............................................................................................................................................................262
Chapter 8 Sampling Distributions
8.1 Distribution of the Sample Mean ....................................................................................................................266
8.2 Distribution of the Sample Proportion ............................................................................................................278
Chapter 8 Review Exercises ......................................................................................................................................284
Chapter 8 Test............................................................................................................................................................287
Chapter 9 Estimating the Value of a Parameter
9.1 Estimating a Population Proportion ................................................................................................................289
9.2 Estimating a Population Mean ........................................................................................................................295
9.3 Putting It Together: Which Procedure Do I Use?............................................................................................305
Chapter 9 Review Exercises ......................................................................................................................................310
Chapter 9 Test............................................................................................................................................................314
Chapter 10 Hypothesis Tests Regarding a Parameter
10.1 The Language of Hypothesis Testing..............................................................................................................317
10.2 Hypothesis Tests for a Population Proportion.................................................................................................320
10.3 Hypothesis Tests for a Population Mean.........................................................................................................329
10.4 Putting It Together: Which Method Do I Use? ...............................................................................................338
Chapter 10 Review Exercises ....................................................................................................................................342
Chapter 10 Test..........................................................................................................................................................346
Chapter 11 Inferences on Two Samples
11.1 Inference about Two Population Proportions..................................................................................................348
11.2 Inference about Two Means: Dependent Samples ..........................................................................................361
11.3 Inference about Two Means: Independent Samples........................................................................................371
11.4 Putting It Together: Which Method Do I Use? ...............................................................................................385
Chapter 11 Review Exercises (Online) ......................................................................................................................398
Chapter 11 Test..........................................................................................................................................................404
Chapter 12 Additional Inferential Techniques
12.1 Goodness-of-Fit Test.......................................................................................................................................410
12.2 Tests for Independence and the Homogeneity of Proportions.........................................................................421
12.3 Testing the Significance of the Least-Squares Regression Model ..................................................................439
12.4 Confidence and Prediction Intervals ...............................................................................................................445
Chapter 12 Review Exercises ....................................................................................................................................451
Chapter 12 Test..........................................................................................................................................................458
6.1 Discrete Random Variables.............................................................................................................................200
6.2 The Binomial Probability Distribution............................................................................................................208
Chapter 6 Review Exercises ......................................................................................................................................222
Chapter 6 Test............................................................................................................................................................225
Chapter 7 The Normal Probability Distribution
7.1 Properties of the Normal Distribution .............................................................................................................228
7.2 Applications of the Normal Distribution.........................................................................................................231
7.3 Assessing Normality .......................................................................................................................................250
7.4 The Normal Approximation to the Binomial Probability Distribution ...........................................................253
Chapter 7 Review Exercises ......................................................................................................................................257
Chapter 7 Test............................................................................................................................................................262
Chapter 8 Sampling Distributions
8.1 Distribution of the Sample Mean ....................................................................................................................266
8.2 Distribution of the Sample Proportion ............................................................................................................278
Chapter 8 Review Exercises ......................................................................................................................................284
Chapter 8 Test............................................................................................................................................................287
Chapter 9 Estimating the Value of a Parameter
9.1 Estimating a Population Proportion ................................................................................................................289
9.2 Estimating a Population Mean ........................................................................................................................295
9.3 Putting It Together: Which Procedure Do I Use?............................................................................................305
Chapter 9 Review Exercises ......................................................................................................................................310
Chapter 9 Test............................................................................................................................................................314
Chapter 10 Hypothesis Tests Regarding a Parameter
10.1 The Language of Hypothesis Testing..............................................................................................................317
10.2 Hypothesis Tests for a Population Proportion.................................................................................................320
10.3 Hypothesis Tests for a Population Mean.........................................................................................................329
10.4 Putting It Together: Which Method Do I Use? ...............................................................................................338
Chapter 10 Review Exercises ....................................................................................................................................342
Chapter 10 Test..........................................................................................................................................................346
Chapter 11 Inferences on Two Samples
11.1 Inference about Two Population Proportions..................................................................................................348
11.2 Inference about Two Means: Dependent Samples ..........................................................................................361
11.3 Inference about Two Means: Independent Samples........................................................................................371
11.4 Putting It Together: Which Method Do I Use? ...............................................................................................385
Chapter 11 Review Exercises (Online) ......................................................................................................................398
Chapter 11 Test..........................................................................................................................................................404
Chapter 12 Additional Inferential Techniques
12.1 Goodness-of-Fit Test.......................................................................................................................................410
12.2 Tests for Independence and the Homogeneity of Proportions.........................................................................421
12.3 Testing the Significance of the Least-Squares Regression Model ..................................................................439
12.4 Confidence and Prediction Intervals ...............................................................................................................445
Chapter 12 Review Exercises ....................................................................................................................................451
Chapter 12 Test..........................................................................................................................................................458
Chapter 1
Data Collection
Section 1.1
1. Statistics is the science of collecting,
organizing, summarizing, and analyzing
information in order to draw conclusions and
answer questions. In addition, statistics is
about providing a measure of confidence in
any conclusions.
2. The population is the group to be studied as
defined by the research objective. A sample is
any subset of the population.
3. Individual
4. Descriptive; Inferential
5. Statistic; Parameter
6. Variables
7. 18% is a parameter because it describes a
population (all of the governors).
8. 72% is a parameter because it describes a
population (the entire class).
9. 32% is a statistic because it describes a sample
(the high school students surveyed).
10. 9.6% is a statistic because it describes a
sample (the youths surveyed).
11. 0.366 is a parameter because it describes a
population (all of Ty Cobb’s at-bats).
12. 43.92 hours is a parameter because it describes
a population (all the men who have walked on
the moon).
13. 23% is a statistic because it describes a sample
(the 6076 adults studied).
14. 44% is a statistic because it describes a sample
(the 100 adults interviewed).
15. Qualitative 16. Quantitative
17. Quantitative 18. Qualitative
19. Quantitative 20. Quantitative
21. Qualitative 22. Qualitative
23. Discrete 24. Continuous
25. Continuous 26. Discrete
27. Continuous 28. Continuous
29. Discrete 30. Continuous
31. Nominal 32. Ordinal
33. Ratio 34. Interval
35. Ordinal 36. Nominal
37. Ratio 38. Interval
39. The population consists of all teenagers 13 to
17 years old who live in the United States.
The sample consists of the 1028 teenagers 13
to 17 years old who were contacted by the
Gallup Organization.
40. The population consists of all bottles of Coca-
Cola filled by that particular machine on
October 15. The sample consists of the
50 bottles of Coca-Cola that were selected by
the quality control manager.
41. The population consists of all of the soybean
plants in this farmer’s crop. The sample
consists of the 100 soybean plants that were
selected by the farmer.
42. The population consists of all households
within the United States. The sample consists
of the 50,000 households that are surveyed by
the U.S. Census Bureau.
43. The population consists of all women 27 to
44 years of age with hypertension. The
sample consists of the 7373 women 27 to 44
years of age with hypertension who were
included in the study.
44. The population consists of all full-time
students enrolled at this large community
college. The sample consists of the 128 full-
time students who were surveyed by the
administration.
Data Collection
Section 1.1
1. Statistics is the science of collecting,
organizing, summarizing, and analyzing
information in order to draw conclusions and
answer questions. In addition, statistics is
about providing a measure of confidence in
any conclusions.
2. The population is the group to be studied as
defined by the research objective. A sample is
any subset of the population.
3. Individual
4. Descriptive; Inferential
5. Statistic; Parameter
6. Variables
7. 18% is a parameter because it describes a
population (all of the governors).
8. 72% is a parameter because it describes a
population (the entire class).
9. 32% is a statistic because it describes a sample
(the high school students surveyed).
10. 9.6% is a statistic because it describes a
sample (the youths surveyed).
11. 0.366 is a parameter because it describes a
population (all of Ty Cobb’s at-bats).
12. 43.92 hours is a parameter because it describes
a population (all the men who have walked on
the moon).
13. 23% is a statistic because it describes a sample
(the 6076 adults studied).
14. 44% is a statistic because it describes a sample
(the 100 adults interviewed).
15. Qualitative 16. Quantitative
17. Quantitative 18. Qualitative
19. Quantitative 20. Quantitative
21. Qualitative 22. Qualitative
23. Discrete 24. Continuous
25. Continuous 26. Discrete
27. Continuous 28. Continuous
29. Discrete 30. Continuous
31. Nominal 32. Ordinal
33. Ratio 34. Interval
35. Ordinal 36. Nominal
37. Ratio 38. Interval
39. The population consists of all teenagers 13 to
17 years old who live in the United States.
The sample consists of the 1028 teenagers 13
to 17 years old who were contacted by the
Gallup Organization.
40. The population consists of all bottles of Coca-
Cola filled by that particular machine on
October 15. The sample consists of the
50 bottles of Coca-Cola that were selected by
the quality control manager.
41. The population consists of all of the soybean
plants in this farmer’s crop. The sample
consists of the 100 soybean plants that were
selected by the farmer.
42. The population consists of all households
within the United States. The sample consists
of the 50,000 households that are surveyed by
the U.S. Census Bureau.
43. The population consists of all women 27 to
44 years of age with hypertension. The
sample consists of the 7373 women 27 to 44
years of age with hypertension who were
included in the study.
44. The population consists of all full-time
students enrolled at this large community
college. The sample consists of the 128 full-
time students who were surveyed by the
administration.
2 Chapter 1: Data Collection
45. Individuals: Alabama, Colorado, Indiana,
North Carolina, Wisconsin.
Variables: Minimum age for driver’s license
(unrestricted); mandatory belt use seating
positions, maximum allowable speed limit
(rural interstate) in 2011.
Data for minimum age for driver’s license:
17, 17, 18, 16, 18;
Data for mandatory belt use seating positions:
front, front, all, all, all;
Data for maximum allowable speed limit
(rural interstate) 2011: 70, 75, 70, 70, 65
(mph.)
The variable minimum age for driver’s license
is continuous; the variable mandatory belt use
seating positions is qualitative; the variable
maximum allowable speed limit (rural
interstate) 2011 is continuous (although only
discrete values are typically chosen for speed
limits.)
46. Individuals: 3 Series, 5 Series, 6 Series,
7 Series, X3, Z4 Roadster
Variables: Body Style, Weight (lb), Number
of Seats
Data for body style: Coupe, Sedan,
Convertible, Sedan, Sport utility, Roadster
Coupe; Data for weight: 3362, 4056, 4277,
4564, 4012, 3505 (lb);
Data for number of seats: 4, 5, 4, 5, 5, 2. The
variable body style is qualitative; the variable
weight is continuous; the variable number of
seats is discrete.
47. (a) The research objective is to determine if
adolescents aged 18–21 who smoke have
a lower IQ than nonsmokers.
(b) The population is all adolescents aged
18–21. The sample consisted of 20,211
18-year-old Israeli military recruits.
(c) Descriptive statistics: The average IQ of
the smokers was 94, and the average IQ
of nonsmokers was 101.
(d) The conclusion is that individuals with a
lower IQ are more likely to choose to
smoke.
48. (a) The research objective is to determine if
the application of duct tape is as effective
as cryotherapy in the treatment of
common warts.
(b) The population is all people with warts.
The sample consisted of 51 patients with
warts.
(c) Descriptive statistics: 85% of patients in
group 1 and 60% of patients in group 2
had complete resolution of their warts.
(d) The conclusion is that duct tape is
significantly more effective in treating
warts than cryotherapy.
49. (a) The research objective is to determine the
proportion of adult Americans who
believe the federal government wastes
51 cents or more of every dollar.
(b) The population is all adult Americans
aged 18 years or older.
(c) The sample is the 1017 American adults
aged 18 years or older that were
surveyed.
(d) Descriptive statistics: Of the 1017
individuals surveyed, 35% indicated that
51 cents or more is wasted.
(e) From this study, one can infer that 31% to
39% of Americans believe the federal
government wastes much of the money
collected in taxes.
50. (a) The research objective is to determine
what proportion of adults, aged 18 and
over, believe it would be a bad idea to
invest $1000 in the stock market.
(b) The population is all adults aged 18 and
over living in the United States.
(c) The sample is the 1018 adults aged 18 and
over living in the United States who
completed the survey.
(d) Descriptive statistics: Of the 1018 adults
surveyed, 46% believe it would be a bad
idea to invest $1000 in the stock market.
(e) The conclusion is that a little fewer than
half of the adults in the United States
believe investing $1000 in the stock
market is a bad idea.
51. Jersey number is nominal (the numbers
generally indicate a type of position played).
However, if the researcher feels that lower
caliber players received higher numbers, then
jersey number would be ordinal since players
could be ranked by their number.
45. Individuals: Alabama, Colorado, Indiana,
North Carolina, Wisconsin.
Variables: Minimum age for driver’s license
(unrestricted); mandatory belt use seating
positions, maximum allowable speed limit
(rural interstate) in 2011.
Data for minimum age for driver’s license:
17, 17, 18, 16, 18;
Data for mandatory belt use seating positions:
front, front, all, all, all;
Data for maximum allowable speed limit
(rural interstate) 2011: 70, 75, 70, 70, 65
(mph.)
The variable minimum age for driver’s license
is continuous; the variable mandatory belt use
seating positions is qualitative; the variable
maximum allowable speed limit (rural
interstate) 2011 is continuous (although only
discrete values are typically chosen for speed
limits.)
46. Individuals: 3 Series, 5 Series, 6 Series,
7 Series, X3, Z4 Roadster
Variables: Body Style, Weight (lb), Number
of Seats
Data for body style: Coupe, Sedan,
Convertible, Sedan, Sport utility, Roadster
Coupe; Data for weight: 3362, 4056, 4277,
4564, 4012, 3505 (lb);
Data for number of seats: 4, 5, 4, 5, 5, 2. The
variable body style is qualitative; the variable
weight is continuous; the variable number of
seats is discrete.
47. (a) The research objective is to determine if
adolescents aged 18–21 who smoke have
a lower IQ than nonsmokers.
(b) The population is all adolescents aged
18–21. The sample consisted of 20,211
18-year-old Israeli military recruits.
(c) Descriptive statistics: The average IQ of
the smokers was 94, and the average IQ
of nonsmokers was 101.
(d) The conclusion is that individuals with a
lower IQ are more likely to choose to
smoke.
48. (a) The research objective is to determine if
the application of duct tape is as effective
as cryotherapy in the treatment of
common warts.
(b) The population is all people with warts.
The sample consisted of 51 patients with
warts.
(c) Descriptive statistics: 85% of patients in
group 1 and 60% of patients in group 2
had complete resolution of their warts.
(d) The conclusion is that duct tape is
significantly more effective in treating
warts than cryotherapy.
49. (a) The research objective is to determine the
proportion of adult Americans who
believe the federal government wastes
51 cents or more of every dollar.
(b) The population is all adult Americans
aged 18 years or older.
(c) The sample is the 1017 American adults
aged 18 years or older that were
surveyed.
(d) Descriptive statistics: Of the 1017
individuals surveyed, 35% indicated that
51 cents or more is wasted.
(e) From this study, one can infer that 31% to
39% of Americans believe the federal
government wastes much of the money
collected in taxes.
50. (a) The research objective is to determine
what proportion of adults, aged 18 and
over, believe it would be a bad idea to
invest $1000 in the stock market.
(b) The population is all adults aged 18 and
over living in the United States.
(c) The sample is the 1018 adults aged 18 and
over living in the United States who
completed the survey.
(d) Descriptive statistics: Of the 1018 adults
surveyed, 46% believe it would be a bad
idea to invest $1000 in the stock market.
(e) The conclusion is that a little fewer than
half of the adults in the United States
believe investing $1000 in the stock
market is a bad idea.
51. Jersey number is nominal (the numbers
generally indicate a type of position played).
However, if the researcher feels that lower
caliber players received higher numbers, then
jersey number would be ordinal since players
could be ranked by their number.
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Section 1.2: Observational Studies vs. Designed Experiments 3
52. (a) Nominal; the ticket number is categorized
as a winner or a loser.
(b) Ordinal; the ticket number gives an
indication as to the order of arrival of
guests.
(c) Ratio; the implication is that the ticket
number gives an indication of the number
of people attending the party.
53. (a) The research question is to determine if
the season of birth affects mood later in
life.
(b) The sample consisted of the 400 people
the researchers studied.
(c) The season in which you were born
(winter, spring, summer, or fall) is a
qualitative variable.
(d) According to the article, individuals born
in the summer are characterized by rapid,
frequent swings between sad and cheerful
moods, while those born in the winter are
less likely to be irritable.
(e) The conclusion was that the season at
birth plays a role in one’s temperament.
54. Quantitative variables are numerical measures
such that meaningful arithmetic operations can
be performed on the values of the variable.
Qualitative variables describe an attribute or
characteristic of the individual that allows
researchers to categorize the individual.
55. The values of a discrete random variable result
from counting. The values of a continuous
random variable result from a measurement.
56. The four levels of measurement of a variable
are nominal, ordinal, interval, and ratio.
Examples: Nominal—brand of clothing;
Ordinal—size of a car (small, mid-size, large);
Interval—temperature (in degrees Celsius);
Ratio—number of students in a class
(Examples will vary.)
57. We say data vary, because when we draw a
random sample from a population, we do not
know which individuals will be included. If
we were to take another random sample, we
would have different individuals and therefore
different data. This variability affects the
results of a statistical analysis because the
results would differ if a study is repeated.
58. The process of statistics is to (1) identify the
research objective, which means to determine
what should be studied and what we hope to
learn; (2) collect the data needed to answer the
research question, which is typically done by
taking a random sample from a population; (3)
describe the data, which is done by presenting
descriptive statistics; and (4) perform
inference in which the results are generalized
to a larger population.
59. Age could be considered a discrete random
variable. A random variable can be discrete
by allowing, for example, only whole numbers
to be recorded.
Section 1.2
1. The response variable is the variable of
interest in a research study. An explanatory
variable is a variable that affects (or explains)
the value of the response variable. In research,
we want to see how changes in the value of
the explanatory variable affect the value of the
response variable.
2. An observational study uses data obtained by
studying individuals in a sample without
trying to manipulate or influence the
variable(s) of interest. In a designed
experiment, a treatment is applied to the
individuals in a sample in order to isolate the
effects of the treatment on a response variable.
Only an experiment can establish causation
between an explanatory variable and a
response variable. Observational studies can
indicate a relationship, but cannot establish
causation.
3. Confounding exists in a study when the effects
of two or more explanatory variables are not
separated. So any relation that appears to exist
between a certain explanatory variable and the
response variable may be due to some other
variable or variables not accounted for in the
study. A lurking variable is a variable not
accounted for in a study, but one that affects
the value of the response variable. A
confounding variable is an explanatory
variable that was considered in a study whose
effect cannot be distinguished from a second
explanatory variable in the study.
52. (a) Nominal; the ticket number is categorized
as a winner or a loser.
(b) Ordinal; the ticket number gives an
indication as to the order of arrival of
guests.
(c) Ratio; the implication is that the ticket
number gives an indication of the number
of people attending the party.
53. (a) The research question is to determine if
the season of birth affects mood later in
life.
(b) The sample consisted of the 400 people
the researchers studied.
(c) The season in which you were born
(winter, spring, summer, or fall) is a
qualitative variable.
(d) According to the article, individuals born
in the summer are characterized by rapid,
frequent swings between sad and cheerful
moods, while those born in the winter are
less likely to be irritable.
(e) The conclusion was that the season at
birth plays a role in one’s temperament.
54. Quantitative variables are numerical measures
such that meaningful arithmetic operations can
be performed on the values of the variable.
Qualitative variables describe an attribute or
characteristic of the individual that allows
researchers to categorize the individual.
55. The values of a discrete random variable result
from counting. The values of a continuous
random variable result from a measurement.
56. The four levels of measurement of a variable
are nominal, ordinal, interval, and ratio.
Examples: Nominal—brand of clothing;
Ordinal—size of a car (small, mid-size, large);
Interval—temperature (in degrees Celsius);
Ratio—number of students in a class
(Examples will vary.)
57. We say data vary, because when we draw a
random sample from a population, we do not
know which individuals will be included. If
we were to take another random sample, we
would have different individuals and therefore
different data. This variability affects the
results of a statistical analysis because the
results would differ if a study is repeated.
58. The process of statistics is to (1) identify the
research objective, which means to determine
what should be studied and what we hope to
learn; (2) collect the data needed to answer the
research question, which is typically done by
taking a random sample from a population; (3)
describe the data, which is done by presenting
descriptive statistics; and (4) perform
inference in which the results are generalized
to a larger population.
59. Age could be considered a discrete random
variable. A random variable can be discrete
by allowing, for example, only whole numbers
to be recorded.
Section 1.2
1. The response variable is the variable of
interest in a research study. An explanatory
variable is a variable that affects (or explains)
the value of the response variable. In research,
we want to see how changes in the value of
the explanatory variable affect the value of the
response variable.
2. An observational study uses data obtained by
studying individuals in a sample without
trying to manipulate or influence the
variable(s) of interest. In a designed
experiment, a treatment is applied to the
individuals in a sample in order to isolate the
effects of the treatment on a response variable.
Only an experiment can establish causation
between an explanatory variable and a
response variable. Observational studies can
indicate a relationship, but cannot establish
causation.
3. Confounding exists in a study when the effects
of two or more explanatory variables are not
separated. So any relation that appears to exist
between a certain explanatory variable and the
response variable may be due to some other
variable or variables not accounted for in the
study. A lurking variable is a variable not
accounted for in a study, but one that affects
the value of the response variable. A
confounding variable is an explanatory
variable that was considered in a study whose
effect cannot be distinguished from a second
explanatory variable in the study.
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4 Chapter 1: Data Collection
4. The choice between an observational study
and an experiment depends on the
circumstances involved. Sometimes there are
ethical reasons why an experiment cannot be
conducted. Other times the researcher may
conduct an observational study first to validate
a belief prior to investing a large amount of
time and money into a designed experiment. A
designed experiment is preferred if ethics,
time, and money are not an issue.
5. Cross-sectional studies collect information at a
specific point in time (or over a very short
period of time). Case-control studies are
retrospective (they look back in time). Also,
individuals that have a certain characteristic
(such as cancer) in a case-control study are
matched with those that do not have the
characteristic. Case-control studies are
typically superior to cross-sectional studies.
They are relatively inexpensive, provide
individual level data, and give longitudinal
information not available in a cross-sectional
study.
6. A cohort study identifies the individuals to
participate and then follows them over a
period of time. During this period, information
about the individuals is gathered, but there is
no attempt to influence the individuals. Cohort
studies are superior to case-control studies
because cohort studies do not require recall to
obtain the data.
7. There is a perceived benefit to obtaining a flu
shot, so there are ethical issues in intentionally
denying certain seniors access to the
treatment.
8. A retrospective study looks at data from the
past either through recall or existing records.
A prospective study gathers data over time by
following the individuals in the study and
recording data as they occur.
9. This is an observational study because the
researchers merely observed existing data.
There was no attempt by the researchers to
manipulate or influence the variable(s) of
interest.
10. This is an experiment because the researchers
intentionally changed the value of the
explanatory variable (medication dose) to
observe a potential effect on the response
variable (cancer growth).
11. This is an experiment because the explanatory
variable (teaching method) was intentionally
varied to see how it affected the response
variable (score on proficiency test).
12. This is an observational study because no
attempt was made to influence the variable of
interest. Voting choices were merely
observed.
13. This is an observational study because the
survey only observed preference of Coke or
Pepsi. No attempt was made to manipulate or
influence the variable of interest.
14. This is an experiment because the researcher
intentionally imposed treatments on
individuals in a controlled setting.
15. This is an experiment because the explanatory
variable (carpal tunnel treatment regimen) was
intentionally manipulated in order to observe
potential effects on the response variable
(level of pain).
16. This is an observational study because the
conservation agents merely observed the fish
to determine which were carrying parasites.
No attempt was made to manipulate or
influence any variable of interest.
17. (a) This is a cohort study because the
researchers observed a group of people
over a period of time.
(b) The response variable is whether the
individual has heart disease or not. The
explanatory variable is whether the
individual is happy or not.
(c) There may be confounding due to lurking
variables. For example, happy people
may be more likely to exercise, which
could affect whether they will have heart
disease or not.
18. (a) This is a cross-sectional study because
the researchers collected information
about the individuals at a specific point in
time.
(b) The response variable is whether the
woman has nonmelanoma skin cancer or
not. The explanatory variable is the daily
amount of caffeinated coffee consumed.
(c) It was necessary to account for these
variables to avoid confounding with other
variables.
4. The choice between an observational study
and an experiment depends on the
circumstances involved. Sometimes there are
ethical reasons why an experiment cannot be
conducted. Other times the researcher may
conduct an observational study first to validate
a belief prior to investing a large amount of
time and money into a designed experiment. A
designed experiment is preferred if ethics,
time, and money are not an issue.
5. Cross-sectional studies collect information at a
specific point in time (or over a very short
period of time). Case-control studies are
retrospective (they look back in time). Also,
individuals that have a certain characteristic
(such as cancer) in a case-control study are
matched with those that do not have the
characteristic. Case-control studies are
typically superior to cross-sectional studies.
They are relatively inexpensive, provide
individual level data, and give longitudinal
information not available in a cross-sectional
study.
6. A cohort study identifies the individuals to
participate and then follows them over a
period of time. During this period, information
about the individuals is gathered, but there is
no attempt to influence the individuals. Cohort
studies are superior to case-control studies
because cohort studies do not require recall to
obtain the data.
7. There is a perceived benefit to obtaining a flu
shot, so there are ethical issues in intentionally
denying certain seniors access to the
treatment.
8. A retrospective study looks at data from the
past either through recall or existing records.
A prospective study gathers data over time by
following the individuals in the study and
recording data as they occur.
9. This is an observational study because the
researchers merely observed existing data.
There was no attempt by the researchers to
manipulate or influence the variable(s) of
interest.
10. This is an experiment because the researchers
intentionally changed the value of the
explanatory variable (medication dose) to
observe a potential effect on the response
variable (cancer growth).
11. This is an experiment because the explanatory
variable (teaching method) was intentionally
varied to see how it affected the response
variable (score on proficiency test).
12. This is an observational study because no
attempt was made to influence the variable of
interest. Voting choices were merely
observed.
13. This is an observational study because the
survey only observed preference of Coke or
Pepsi. No attempt was made to manipulate or
influence the variable of interest.
14. This is an experiment because the researcher
intentionally imposed treatments on
individuals in a controlled setting.
15. This is an experiment because the explanatory
variable (carpal tunnel treatment regimen) was
intentionally manipulated in order to observe
potential effects on the response variable
(level of pain).
16. This is an observational study because the
conservation agents merely observed the fish
to determine which were carrying parasites.
No attempt was made to manipulate or
influence any variable of interest.
17. (a) This is a cohort study because the
researchers observed a group of people
over a period of time.
(b) The response variable is whether the
individual has heart disease or not. The
explanatory variable is whether the
individual is happy or not.
(c) There may be confounding due to lurking
variables. For example, happy people
may be more likely to exercise, which
could affect whether they will have heart
disease or not.
18. (a) This is a cross-sectional study because
the researchers collected information
about the individuals at a specific point in
time.
(b) The response variable is whether the
woman has nonmelanoma skin cancer or
not. The explanatory variable is the daily
amount of caffeinated coffee consumed.
(c) It was necessary to account for these
variables to avoid confounding with other
variables.
Loading page 8...
Section 1.2: Observational Studies vs. Designed Experiments 5
19. (a) This is an observational study because the
researchers simply administered a
questionnaire to obtain their data. No
attempt was made to manipulate or
influence the variable(s) of interest.
This is a cross-sectional study because
the researchers are observing participants
at a single point in time.
(b) The response variable is body mass
index. The explanatory variable is
whether a TV is in the bedroom or not.
(c) Answers will vary. Some lurking
variables might be the amount of exercise
per week and eating habits. Both of these
variables can affect the body mass index
of an individual.
(d) The researchers attempted to avoid
confounding due to other variables by
taking into account such variables as
“socioeconomic status.”
(e) No. Since this was an observational
study, we can only say that a television in
the bedroom is associated with a higher
body mass index.
20. (a) This is an observational study because the
researchers merely observed the
individuals included in the study. No
attempt was made to manipulate or
influence any variable of interest.
This is a cohort study because the
researchers identified the individuals to
be included in the study, then followed
them for a period of time (7 years).
(b) The response variable is weight gain. The
explanatory variable is whether the
individual is married/cohabitating or not.
(c) Answers will vary. Some potential
lurking variables are eating habits,
exercise routine, and whether the
individual has children.
(d) No. Since this is an observational study,
we can only say that being married or
cohabitating is associated with weight
gain.
21. (a) This is a cross-sectional study because
information was collected at a specific
point in time (or over a very short period
of time).
(b) The explanatory variable is delivery
scenario (caseload midwifery, standard
hospital care, or private obstetric care).
(c) The two response variables are (1) cost of
delivery, which is quantitative, and (2)
type of delivery (vaginal or not), which is
quantitative.
22. (a) The explanatory variable is web page
design; qualitative
(b) The response variables are time on site
and amount spent. Both are quantitative.
(c) Answers will vary. A confounding
variable might be location. Any
differences in spending may be due to
location rather than to web page design.
23. Answers will vary. This is a prospective,
cohort observational study. The response
variable is whether the worker had cancer or
not, and the explanatory variable is the amount
of electromagnetic field exposure. Some
possible lurking variables include eating
habits, exercise habits, and other health-related
variables such as smoking habits. Genetics
(family history) could also be a lurking
variable. This was an observational study, and
not an experiment, so the study only concludes
that high electromagnetic field exposure is
associated with higher cancer rates.
The author reminds us that this is an
observational study, so there is no direct
control over the variables that may affect
cancer rates. He also points out that while we
should not simply dismiss such reports, we
should consider the results in conjunction with
results from future studies. The author
concludes by mentioning known ways (based
on extensive study) of reducing cancer risks
that can currently be done in our lives.
24. (a) The research objective is to determine
whether lung cancer is associated with
exposure to tobacco smoke within the
household.
(b) This is a case-controlled study because
there is a group of individuals with a
certain characteristic (lung cancer but
never smoked) being compared to a
similar group without the characteristic
(no lung cancer and never smoked). The
study is retrospective because lifetime
residential histories were compiled and
analyzed.
19. (a) This is an observational study because the
researchers simply administered a
questionnaire to obtain their data. No
attempt was made to manipulate or
influence the variable(s) of interest.
This is a cross-sectional study because
the researchers are observing participants
at a single point in time.
(b) The response variable is body mass
index. The explanatory variable is
whether a TV is in the bedroom or not.
(c) Answers will vary. Some lurking
variables might be the amount of exercise
per week and eating habits. Both of these
variables can affect the body mass index
of an individual.
(d) The researchers attempted to avoid
confounding due to other variables by
taking into account such variables as
“socioeconomic status.”
(e) No. Since this was an observational
study, we can only say that a television in
the bedroom is associated with a higher
body mass index.
20. (a) This is an observational study because the
researchers merely observed the
individuals included in the study. No
attempt was made to manipulate or
influence any variable of interest.
This is a cohort study because the
researchers identified the individuals to
be included in the study, then followed
them for a period of time (7 years).
(b) The response variable is weight gain. The
explanatory variable is whether the
individual is married/cohabitating or not.
(c) Answers will vary. Some potential
lurking variables are eating habits,
exercise routine, and whether the
individual has children.
(d) No. Since this is an observational study,
we can only say that being married or
cohabitating is associated with weight
gain.
21. (a) This is a cross-sectional study because
information was collected at a specific
point in time (or over a very short period
of time).
(b) The explanatory variable is delivery
scenario (caseload midwifery, standard
hospital care, or private obstetric care).
(c) The two response variables are (1) cost of
delivery, which is quantitative, and (2)
type of delivery (vaginal or not), which is
quantitative.
22. (a) The explanatory variable is web page
design; qualitative
(b) The response variables are time on site
and amount spent. Both are quantitative.
(c) Answers will vary. A confounding
variable might be location. Any
differences in spending may be due to
location rather than to web page design.
23. Answers will vary. This is a prospective,
cohort observational study. The response
variable is whether the worker had cancer or
not, and the explanatory variable is the amount
of electromagnetic field exposure. Some
possible lurking variables include eating
habits, exercise habits, and other health-related
variables such as smoking habits. Genetics
(family history) could also be a lurking
variable. This was an observational study, and
not an experiment, so the study only concludes
that high electromagnetic field exposure is
associated with higher cancer rates.
The author reminds us that this is an
observational study, so there is no direct
control over the variables that may affect
cancer rates. He also points out that while we
should not simply dismiss such reports, we
should consider the results in conjunction with
results from future studies. The author
concludes by mentioning known ways (based
on extensive study) of reducing cancer risks
that can currently be done in our lives.
24. (a) The research objective is to determine
whether lung cancer is associated with
exposure to tobacco smoke within the
household.
(b) This is a case-controlled study because
there is a group of individuals with a
certain characteristic (lung cancer but
never smoked) being compared to a
similar group without the characteristic
(no lung cancer and never smoked). The
study is retrospective because lifetime
residential histories were compiled and
analyzed.
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6 Chapter 1: Data Collection
(c) The response variable is whether the
individual has lung cancer or not. This is
a qualitative variable.
(d) The explanatory variable is the number of
“smoker years.” This is a quantitative
variable.
(e) Answers will vary. Some possible
lurking variables are household income,
exercise routine, and exposure to tobacco
smoke outside the home.
(f) The conclusion of the study is that
approximately 17% of lung cancer cases
among nonsmokers can be attributed to
high levels of exposure to tobacco smoke
during childhood and adolescence. No,
we cannot say that exposure to household
tobacco smoke causes lung cancer since
this is only an observational study. We
can, however, conclude that lung cancer
is associated with exposure to tobacco
smoke in the home.
(g) An experiment involving human subjects
is not possible for ethical reasons.
Researchers would be able to conduct an
experiment using laboratory animals,
such as rats.
Section 1.3
1. The frame is a list of all the individuals in the
population.
2. Simple random sampling occurs when every
possible sample of size n has an equally likely
chance of occurring.
3. Sampling without replacement means that no
individual may be selected more than once as
a member of the sample.
4. Random sampling is a technique that uses
chance to select individuals from a population
to be in a sample. It is used because it
maximizes the likelihood that the individuals
in the sample are representative of the
individuals in the population. In convenience
sampling, the individuals in the sample are
selected in the quickest and easiest way
possible (e.g. the first 20 people to enter a
store). Convenience samples likely do not
represent the population of interest because
chance was not used to select the individuals.
5. Answers will vary. We will use one-digit
labels and assign the labels across each row
(i.e. Pride and Prejudice – 0, The Sun Also
Rises – 1, and so on). In Table I of Appendix
A, starting at row 5, column 11, and
proceeding downward, we obtain the
following labels: 8, 4, 3
In this case, the 3 books in the sample would
be As I Lay Dying, A Tale of Two Cities, and
Crime and Punishment. Different labeling
order, different starting points in Table I in
Appendix A, or use of technology will likely
yield different samples.
6. Answers will vary. We will use one-digit
labels and assign the labels across each row
(i.e. Mady – 0, Breanne – 1, and so on). In
Table I of Appendix A, starting at row 11,
column 6, and then proceeding downward, we
obtain the following labels: 1, 5
In this case, the two captains would be
Breanne and Payton. Different labeling order,
different starting points in Table I in
Appendix A, or use of technology will likely
yield different results.
7. (a) {616, 630}, {616, 631}, {616, 632},
{616, 645}, {616, 649}, {616, 650},
{630, 631}, {630, 632}, {630, 645},
{630, 649}, {630, 650}, {631, 632},
{631, 645}, {631, 649}, {631, 650},
{632, 645}, {632, 649}, {632, 650},
{645, 649}, {645, 650}, {649, 650}
(b) There is a 1 in 21 chance that the pair of
courses will be EPR 630 and EPR 645.
8. (a) {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6},
{1, 7}, {2, 3}, {2, 4}, {2, 5}, {2, 6},
{2, 7}, {3, 4}, {3, 5}, {3, 6}, {3, 7},
{4, 5}, {4, 6}, {4, 7}, {5, 6}, {5, 7},
{6, 7}
(b) There is a 1 in 21 chance that the pair
The United Nations and Amnesty
International will be selected.
9. (a) Starting at row 5, column 22, using two-
digit numbers, and proceeding
downward, we obtain the following
values: 83, 94, 67, 84, 38, 22, 96, 24, 36,
36, 58, 34,.... We must disregard 94 and
96 because there are only 87 faculty
members in the population. We must
also disregard the second 36 because we
are sampling without replacement. Thus,
the 9 faculty members included in the
sample are those numbered 83, 67, 84,
38, 22, 24, 36, 58, and 34.
(c) The response variable is whether the
individual has lung cancer or not. This is
a qualitative variable.
(d) The explanatory variable is the number of
“smoker years.” This is a quantitative
variable.
(e) Answers will vary. Some possible
lurking variables are household income,
exercise routine, and exposure to tobacco
smoke outside the home.
(f) The conclusion of the study is that
approximately 17% of lung cancer cases
among nonsmokers can be attributed to
high levels of exposure to tobacco smoke
during childhood and adolescence. No,
we cannot say that exposure to household
tobacco smoke causes lung cancer since
this is only an observational study. We
can, however, conclude that lung cancer
is associated with exposure to tobacco
smoke in the home.
(g) An experiment involving human subjects
is not possible for ethical reasons.
Researchers would be able to conduct an
experiment using laboratory animals,
such as rats.
Section 1.3
1. The frame is a list of all the individuals in the
population.
2. Simple random sampling occurs when every
possible sample of size n has an equally likely
chance of occurring.
3. Sampling without replacement means that no
individual may be selected more than once as
a member of the sample.
4. Random sampling is a technique that uses
chance to select individuals from a population
to be in a sample. It is used because it
maximizes the likelihood that the individuals
in the sample are representative of the
individuals in the population. In convenience
sampling, the individuals in the sample are
selected in the quickest and easiest way
possible (e.g. the first 20 people to enter a
store). Convenience samples likely do not
represent the population of interest because
chance was not used to select the individuals.
5. Answers will vary. We will use one-digit
labels and assign the labels across each row
(i.e. Pride and Prejudice – 0, The Sun Also
Rises – 1, and so on). In Table I of Appendix
A, starting at row 5, column 11, and
proceeding downward, we obtain the
following labels: 8, 4, 3
In this case, the 3 books in the sample would
be As I Lay Dying, A Tale of Two Cities, and
Crime and Punishment. Different labeling
order, different starting points in Table I in
Appendix A, or use of technology will likely
yield different samples.
6. Answers will vary. We will use one-digit
labels and assign the labels across each row
(i.e. Mady – 0, Breanne – 1, and so on). In
Table I of Appendix A, starting at row 11,
column 6, and then proceeding downward, we
obtain the following labels: 1, 5
In this case, the two captains would be
Breanne and Payton. Different labeling order,
different starting points in Table I in
Appendix A, or use of technology will likely
yield different results.
7. (a) {616, 630}, {616, 631}, {616, 632},
{616, 645}, {616, 649}, {616, 650},
{630, 631}, {630, 632}, {630, 645},
{630, 649}, {630, 650}, {631, 632},
{631, 645}, {631, 649}, {631, 650},
{632, 645}, {632, 649}, {632, 650},
{645, 649}, {645, 650}, {649, 650}
(b) There is a 1 in 21 chance that the pair of
courses will be EPR 630 and EPR 645.
8. (a) {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6},
{1, 7}, {2, 3}, {2, 4}, {2, 5}, {2, 6},
{2, 7}, {3, 4}, {3, 5}, {3, 6}, {3, 7},
{4, 5}, {4, 6}, {4, 7}, {5, 6}, {5, 7},
{6, 7}
(b) There is a 1 in 21 chance that the pair
The United Nations and Amnesty
International will be selected.
9. (a) Starting at row 5, column 22, using two-
digit numbers, and proceeding
downward, we obtain the following
values: 83, 94, 67, 84, 38, 22, 96, 24, 36,
36, 58, 34,.... We must disregard 94 and
96 because there are only 87 faculty
members in the population. We must
also disregard the second 36 because we
are sampling without replacement. Thus,
the 9 faculty members included in the
sample are those numbered 83, 67, 84,
38, 22, 24, 36, 58, and 34.
Loading page 10...
Section 1.3: Simple Random Sampling 7
(b) Answers will vary depending on the type
of technology used. If using a TI-84
Plus, the sample will be: 4, 20, 52, 5, 24,
87, 67, 86, and 39.
Note: We must disregard the second 20
because we are sampling without
replacement.
10. (a) Starting at row 11, column 32, using four-
digit numbers, and proceeding
downward, we obtain the following
values: 2869, 5518, 6635, 2182, 8906,
0603, 2654, 2686, 0135, 7783, 4080,
6621, 3774, 7887, 0826, 0916, 3188,
0876, 5418, 0037, 3130, 2882, 0662,….
We must disregard 8906, 7783, and 7887
because there are only 7656 students in
the population.
Thus, the 20 students included in the
sample are those numbered 2869, 5518,
6635, 2182, 0603, 2654, 2686, 0135,
4080, 6621, 3774, 0826, 0916, 3188,
0876, 5418, 0037, 3130, 2882, and 0662.
(b) Answers may vary depending on the type
of technology used. If using a TI-84
Plus, the sample will be: 6658, 4118, 9,
4828, 3905, 454, 2825, 2381, 495, 4445,
4455, 5759, 5397, 7066, 3404, 6667,
5074, 3777, 3206, 5216.
11. (a) Answers will vary depending on the
technology used (including a table of
random digits). Using a TI-84 Plus
graphing calculator with a seed of 17 and
the labels provided, our sample would be
North Dakota, Nevada, Tennessee,
Wisconsin, Minnesota, Maine, New
Hampshire, Florida, Missouri, and
Mississippi.
(b) Repeating part (a) with a seed of 18, our
sample would be Michigan,
Massachusetts, Arizona, Minnesota,
Maine, Nebraska, Georgia, Iowa, Rhode
Island, Indiana.
12. (a) Answers will vary depending on the
technology used (including a table of
random digits). Using a TI-84 Plus
graphing calculator with a seed of 98 and
the labels provided, our sample would be
Jefferson, Carter, Madison, Obama,
Pierce, Buchanan, Ford, Clinton.
(b) Repeating part (a) with a seed of 99, our
sample would be L. B. Johnson, Truman,
Pierce, Garfield, Obama, Grant, George
H. Bush, T. Roosevelt.
13. (a) The list provided by the administration
serves as the frame. Number each student
in the list of registered students, from 1 to
19,935. Generate 25 random numbers,
without repetition, between 1 and 19,935
using a random number generator or
table. Select the 25 students with these
numbers.
(b) Answers will vary.
14. (a) The list provided by the mayor serves as
the frame. Number each resident in the
list supplied by the mayor, from 1 to
5832. Generate 20 random numbers,
without repetition, between 1 and 5832
using a random number generator or
table. Select the 20 residents with these
numbers.
(b) Answers will vary.
15. Answers will vary. Members should be
numbered 1–32, though other numbering
schemes are possible (e.g. 0–31). Using a
table of random digits or a random-number
generator, four different numbers (labels)
should be selected. The names corresponding
to these numbers form the sample.
(b) Answers will vary depending on the type
of technology used. If using a TI-84
Plus, the sample will be: 4, 20, 52, 5, 24,
87, 67, 86, and 39.
Note: We must disregard the second 20
because we are sampling without
replacement.
10. (a) Starting at row 11, column 32, using four-
digit numbers, and proceeding
downward, we obtain the following
values: 2869, 5518, 6635, 2182, 8906,
0603, 2654, 2686, 0135, 7783, 4080,
6621, 3774, 7887, 0826, 0916, 3188,
0876, 5418, 0037, 3130, 2882, 0662,….
We must disregard 8906, 7783, and 7887
because there are only 7656 students in
the population.
Thus, the 20 students included in the
sample are those numbered 2869, 5518,
6635, 2182, 0603, 2654, 2686, 0135,
4080, 6621, 3774, 0826, 0916, 3188,
0876, 5418, 0037, 3130, 2882, and 0662.
(b) Answers may vary depending on the type
of technology used. If using a TI-84
Plus, the sample will be: 6658, 4118, 9,
4828, 3905, 454, 2825, 2381, 495, 4445,
4455, 5759, 5397, 7066, 3404, 6667,
5074, 3777, 3206, 5216.
11. (a) Answers will vary depending on the
technology used (including a table of
random digits). Using a TI-84 Plus
graphing calculator with a seed of 17 and
the labels provided, our sample would be
North Dakota, Nevada, Tennessee,
Wisconsin, Minnesota, Maine, New
Hampshire, Florida, Missouri, and
Mississippi.
(b) Repeating part (a) with a seed of 18, our
sample would be Michigan,
Massachusetts, Arizona, Minnesota,
Maine, Nebraska, Georgia, Iowa, Rhode
Island, Indiana.
12. (a) Answers will vary depending on the
technology used (including a table of
random digits). Using a TI-84 Plus
graphing calculator with a seed of 98 and
the labels provided, our sample would be
Jefferson, Carter, Madison, Obama,
Pierce, Buchanan, Ford, Clinton.
(b) Repeating part (a) with a seed of 99, our
sample would be L. B. Johnson, Truman,
Pierce, Garfield, Obama, Grant, George
H. Bush, T. Roosevelt.
13. (a) The list provided by the administration
serves as the frame. Number each student
in the list of registered students, from 1 to
19,935. Generate 25 random numbers,
without repetition, between 1 and 19,935
using a random number generator or
table. Select the 25 students with these
numbers.
(b) Answers will vary.
14. (a) The list provided by the mayor serves as
the frame. Number each resident in the
list supplied by the mayor, from 1 to
5832. Generate 20 random numbers,
without repetition, between 1 and 5832
using a random number generator or
table. Select the 20 residents with these
numbers.
(b) Answers will vary.
15. Answers will vary. Members should be
numbered 1–32, though other numbering
schemes are possible (e.g. 0–31). Using a
table of random digits or a random-number
generator, four different numbers (labels)
should be selected. The names corresponding
to these numbers form the sample.
Loading page 11...
8 Chapter 1: Data Collection
16. Answers will vary. Employees should be
numbered 1–29, though other numbering
schemes are possible (e.g. 0–28). Using a
table of random digits or a random-number
generator, four different numbers (labels)
should be selected. The names corresponding
to these numbers form the sample.
Section 1.4
1. Stratified random sampling may be
appropriate if the population of interest can be
divided into groups (or strata) that are
homogeneous and nonoverlapping.
2. Systematic sampling does not require a frame.
3. Convenience samples are typically selected in
a nonrandom manner. This means the results
are not likely to represent the population.
Convenience samples may also be self-
selected, which will frequently result in small
portions of the population being
overrepresented.
4. Cluster sample
5. Stratified sample
6. False. In a systematic random sample, every
kth individual is selected from the population.
7. False. In many cases, other sampling
techniques may provide equivalent or more
information about the population with less
“cost” than simple random sampling.
8. True. When the clusters are heterogeneous,
the heterogeneity of each cluster likely
resembles the heterogeneity of the population.
In such cases, fewer clusters with more
individuals from each cluster are preferred.
9. True. Because the individuals in a
convenience sample are not selected using
chance, it is likely that the sample is not
representative of the population.
10. False. With stratified samples, the number of
individuals sampled from each strata should
be proportional to the size of the strata in the
population.
11. Systematic sampling. The quality-control
manager is sampling every 8 th chip, starting
with the 3 rd chip.
12. Cluster sampling. The commission tests all
members of the selected teams (clusters).
13. Cluster sampling. The airline surveys all
passengers on selected flights (clusters).
14. Stratified sampling. The congresswoman
samples some individuals from each of three
different income brackets (strata).
15. Simple random sampling. Each known user of
the product has the same chance of being
included in the sample.
16. Convenience sampling. The radio station is
relying on voluntary response to obtain the
sample data.
17. Cluster sampling. The farmer samples all
trees within the selected subsections (clusters).
18. Stratified sampling. The school official takes a
sample of students from each of the five
classes (strata).
19. Convenience sampling. The research firm is
relying on voluntary response to obtain the
sample data.
20. Systematic sampling. The presider is sampling
every 5 th person attending the lecture, starting
with the 3 rd person.
21. Stratified sampling. Shawn takes a sample of
measurements during each of the four time
intervals (strata).
22. Simple random sampling. Each club member
has the same chance of being selected for the
survey.
23. The numbers corresponding to the 20 clients
selected are 16 , 16 25 41+ = , 41 25 66+ = ,
66 25 91+ = , 91 25 116+ = , 141, 166, 191,
216, 241, 266, 291, 316, 341, 366, 391, 416,
441, 466, 491.
24. Since the number of clusters is more than 100,
but less than 1000, we assign each cluster a
three-digit label between 001 and 795.
Starting at row 8, column 38 in Table I of
Appendix A, and proceeding downward, the
10 clusters selected are numbered 763, 185,
377, 304, 626, 392, 315, 084, 565, and 508.
Note that we discard 822 and 955 in reading
the table because we have no clusters with
these labels. We also discard the second
occurrence of 377 because we cannot select
the same cluster twice.
16. Answers will vary. Employees should be
numbered 1–29, though other numbering
schemes are possible (e.g. 0–28). Using a
table of random digits or a random-number
generator, four different numbers (labels)
should be selected. The names corresponding
to these numbers form the sample.
Section 1.4
1. Stratified random sampling may be
appropriate if the population of interest can be
divided into groups (or strata) that are
homogeneous and nonoverlapping.
2. Systematic sampling does not require a frame.
3. Convenience samples are typically selected in
a nonrandom manner. This means the results
are not likely to represent the population.
Convenience samples may also be self-
selected, which will frequently result in small
portions of the population being
overrepresented.
4. Cluster sample
5. Stratified sample
6. False. In a systematic random sample, every
kth individual is selected from the population.
7. False. In many cases, other sampling
techniques may provide equivalent or more
information about the population with less
“cost” than simple random sampling.
8. True. When the clusters are heterogeneous,
the heterogeneity of each cluster likely
resembles the heterogeneity of the population.
In such cases, fewer clusters with more
individuals from each cluster are preferred.
9. True. Because the individuals in a
convenience sample are not selected using
chance, it is likely that the sample is not
representative of the population.
10. False. With stratified samples, the number of
individuals sampled from each strata should
be proportional to the size of the strata in the
population.
11. Systematic sampling. The quality-control
manager is sampling every 8 th chip, starting
with the 3 rd chip.
12. Cluster sampling. The commission tests all
members of the selected teams (clusters).
13. Cluster sampling. The airline surveys all
passengers on selected flights (clusters).
14. Stratified sampling. The congresswoman
samples some individuals from each of three
different income brackets (strata).
15. Simple random sampling. Each known user of
the product has the same chance of being
included in the sample.
16. Convenience sampling. The radio station is
relying on voluntary response to obtain the
sample data.
17. Cluster sampling. The farmer samples all
trees within the selected subsections (clusters).
18. Stratified sampling. The school official takes a
sample of students from each of the five
classes (strata).
19. Convenience sampling. The research firm is
relying on voluntary response to obtain the
sample data.
20. Systematic sampling. The presider is sampling
every 5 th person attending the lecture, starting
with the 3 rd person.
21. Stratified sampling. Shawn takes a sample of
measurements during each of the four time
intervals (strata).
22. Simple random sampling. Each club member
has the same chance of being selected for the
survey.
23. The numbers corresponding to the 20 clients
selected are 16 , 16 25 41+ = , 41 25 66+ = ,
66 25 91+ = , 91 25 116+ = , 141, 166, 191,
216, 241, 266, 291, 316, 341, 366, 391, 416,
441, 466, 491.
24. Since the number of clusters is more than 100,
but less than 1000, we assign each cluster a
three-digit label between 001 and 795.
Starting at row 8, column 38 in Table I of
Appendix A, and proceeding downward, the
10 clusters selected are numbered 763, 185,
377, 304, 626, 392, 315, 084, 565, and 508.
Note that we discard 822 and 955 in reading
the table because we have no clusters with
these labels. We also discard the second
occurrence of 377 because we cannot select
the same cluster twice.
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Section 1.4: Other Effective Sampling Methods 9
25. Answers will vary. To obtain the sample,
number the Democrats 1 to 16 and obtain a
simple random sample of size 2. Then number
the Republicans 1 to 16 and obtain a simple
random sample of size 2. Be sure to use a
different starting point in Table I or a different
seed for each stratum.
For example, using a TI-84 Plus graphing
calculator with a seed of 38 for the Democrats
and 40 for the Republicans, the numbers
selected would be 6, 9 for the Democrats and
14, 4 for the Republicans. If we had numbered
the individuals down each column, the sample
would consist of Haydra, Motola, Thompson,
and Engler.
26. Answers will vary. To obtain the sample,
number the managers 1 to 8 and obtain a
simple random sample of size 2. Then number
the employees 1 to 21 and obtain a simple
random sample of size 4. Be sure to use a
different starting point in Table I or a different
seed for each stratum.
For example, using a TI-84 Plus graphing
calculator with a seed of 18 for the managers
and 20 for the employees, the numbers
selected would be 4, 1 for the managers and
20, 3, 11, 9 for the employees. If we had
numbered the individuals down each column,
the sample would consist of Lindsey, Carlisle,
Weber, Bryant, Hall, and Gow.
27. (a) 4502 90.04 90
50
N
n = = → ; Thus, 90k = .
(b) Randomly select a number between 1 and
90. Suppose that we select 15. Then the
individuals to be surveyed will be the
15th, 105th, 195th, 285th, and so on up to
the 4425th employee on the company list.
28. (a) 945035 7269.5 7269
130
N
n = = → ; Thus,
7269k = .
(b) Randomly select a number between 1 and
7269. Suppose that we randomly select
2000. Then we will survey the
individuals numbered 2000, 9269,
16,538, and so on up to the individual
numbered 939,701.
29. Simple Random Sample:
Number the students from 1 to 1280. Use
a table of random digits or a random-
number generator to randomly select 128
students to survey.
Stratified Sample:
Since class sizes are similar, we would
want to randomly select 128 4
32 =
students from each class to be included in
the sample.
Cluster Sample:
Since classes are similar in size and
makeup, we would want to randomly
select 128 4
32 = classes and include all the
students from those classes in the sample.
30. No. The clusters were not randomly selected.
This would be considered convenience
sampling.
31. Answers will vary. One design would be a
stratified random sample, with two strata
being commuters and noncommuters, as these
two groups each might be fairly homogeneous
in their reactions to the proposal.
32. Answers will vary. One design would be a
cluster sample, with classes as the clusters.
Randomly select clusters and then survey all
the students in the selected classes. However,
care would need to be taken to make sure that
no one was polled twice. Since this would
negate some of the ease of cluster sampling, a
simple random sample might be the more
suitable design.
33. Answers will vary. One design would be a
cluster sample, with the clusters being city
blocks. Randomly select city blocks and
survey every household in the selected blocks.
34. Answers will vary. One appropriate design
would be a systematic sample, after doing a
random start, clocking the speed of every
tenth car, for example.
25. Answers will vary. To obtain the sample,
number the Democrats 1 to 16 and obtain a
simple random sample of size 2. Then number
the Republicans 1 to 16 and obtain a simple
random sample of size 2. Be sure to use a
different starting point in Table I or a different
seed for each stratum.
For example, using a TI-84 Plus graphing
calculator with a seed of 38 for the Democrats
and 40 for the Republicans, the numbers
selected would be 6, 9 for the Democrats and
14, 4 for the Republicans. If we had numbered
the individuals down each column, the sample
would consist of Haydra, Motola, Thompson,
and Engler.
26. Answers will vary. To obtain the sample,
number the managers 1 to 8 and obtain a
simple random sample of size 2. Then number
the employees 1 to 21 and obtain a simple
random sample of size 4. Be sure to use a
different starting point in Table I or a different
seed for each stratum.
For example, using a TI-84 Plus graphing
calculator with a seed of 18 for the managers
and 20 for the employees, the numbers
selected would be 4, 1 for the managers and
20, 3, 11, 9 for the employees. If we had
numbered the individuals down each column,
the sample would consist of Lindsey, Carlisle,
Weber, Bryant, Hall, and Gow.
27. (a) 4502 90.04 90
50
N
n = = → ; Thus, 90k = .
(b) Randomly select a number between 1 and
90. Suppose that we select 15. Then the
individuals to be surveyed will be the
15th, 105th, 195th, 285th, and so on up to
the 4425th employee on the company list.
28. (a) 945035 7269.5 7269
130
N
n = = → ; Thus,
7269k = .
(b) Randomly select a number between 1 and
7269. Suppose that we randomly select
2000. Then we will survey the
individuals numbered 2000, 9269,
16,538, and so on up to the individual
numbered 939,701.
29. Simple Random Sample:
Number the students from 1 to 1280. Use
a table of random digits or a random-
number generator to randomly select 128
students to survey.
Stratified Sample:
Since class sizes are similar, we would
want to randomly select 128 4
32 =
students from each class to be included in
the sample.
Cluster Sample:
Since classes are similar in size and
makeup, we would want to randomly
select 128 4
32 = classes and include all the
students from those classes in the sample.
30. No. The clusters were not randomly selected.
This would be considered convenience
sampling.
31. Answers will vary. One design would be a
stratified random sample, with two strata
being commuters and noncommuters, as these
two groups each might be fairly homogeneous
in their reactions to the proposal.
32. Answers will vary. One design would be a
cluster sample, with classes as the clusters.
Randomly select clusters and then survey all
the students in the selected classes. However,
care would need to be taken to make sure that
no one was polled twice. Since this would
negate some of the ease of cluster sampling, a
simple random sample might be the more
suitable design.
33. Answers will vary. One design would be a
cluster sample, with the clusters being city
blocks. Randomly select city blocks and
survey every household in the selected blocks.
34. Answers will vary. One appropriate design
would be a systematic sample, after doing a
random start, clocking the speed of every
tenth car, for example.
Loading page 13...
10 Chapter 1: Data Collection
35. Answers will vary. Since the company
already has a list (frame) of 6600 individuals
with high cholesterol, a simple random sample
would be an appropriate design.
36. Answers will vary. Since a list of all the
households in the population exists, a simple
random sample is possible. Number the
households from 1 to N, then use a table of
random digits or a random-number generator
to select the sample.
37. (a) For a political poll, a good frame would
be all registered voters who have voted in
the past few elections since they are more
likely to vote in upcoming elections.
(b) Because each individual from the frame
has the same chance of being selected,
there is a possibility that one group may
be over- or underrepresented.
(c) By using a stratified sample, the strategist
can obtain a simple random sample
within each strata (political party) so that
the number of individuals in the sample is
proportionate to the number of
individuals in the population.
38. Random sampling means that the individuals
chosen to be in the sample are selected by
chance. Random sampling minimizes the
chance that one part of the population is over-
or underrepresented in the sample. However,
it cannot guarantee that the sample will
accurately represent the population.
39. Answers will vary.
40. Answers will vary.
Section 1.5
1. A closed question is one in which the
respondent must choose from a list of
prescribed responses. An open question is one
in which the respondent is free to choose his
or her own response. Closed questions are
easier to analyze, but limit the responses.
Open questions allow respondents to state
exactly how they feel, but are harder to
analyze due to the variety of answers and
possible misinterpretation of answers.
2. A certain segment of the population is
underrepresented if it is represented in the
sample in a lower proportion than its size in
the population.
3. Bias means that the results of the sample are
not representative of the population. There are
three types of bias: sampling bias, response
bias, and nonresponse bias. Sampling bias is
due to the use of a sample to describe a
population. This includes bias due to
convenience sampling. Response bias
involves intentional or unintentional
misinformation. This would include lying to a
surveyor or entering responses incorrectly.
Nonresponse bias results when individuals
choose not to respond to questions or are
unable to be reached. A census can suffer
from response bias and nonresponse bias, but
would not suffer from sampling bias.
4. Nonsampling error is the error that results
from undercoverage, nonresponse bias,
response bias, or data-entry errors. Essentially,
it is the error that results from the process of
obtaining and recording data. Sampling error
is the error that results because a sample is
being used to estimate information about a
population. Any error that could also occur in
a census is considered a nonsampling error.
5. (a) Sampling bias. The survey suffers from
undercoverage because the first
60 customers are likely not
representative of the entire customer
population.
(b) Since a complete frame is not possible,
systematic random sampling could be
used to make the sample more
representative of the customer population.
6. (a) Sampling bias. The survey suffers from
undercoverage because only homes in the
southwest corner have a chance to be
interviewed. These homes may have
different demographics than those in
other parts of the village.
(b) Assuming that households within any
given neighborhood have similar
household incomes, stratified sampling
might be appropriate, with neighborhoods
as the strata.
7. (a) Response bias. The survey suffers from
response bias because the question is
poorly worded.
35. Answers will vary. Since the company
already has a list (frame) of 6600 individuals
with high cholesterol, a simple random sample
would be an appropriate design.
36. Answers will vary. Since a list of all the
households in the population exists, a simple
random sample is possible. Number the
households from 1 to N, then use a table of
random digits or a random-number generator
to select the sample.
37. (a) For a political poll, a good frame would
be all registered voters who have voted in
the past few elections since they are more
likely to vote in upcoming elections.
(b) Because each individual from the frame
has the same chance of being selected,
there is a possibility that one group may
be over- or underrepresented.
(c) By using a stratified sample, the strategist
can obtain a simple random sample
within each strata (political party) so that
the number of individuals in the sample is
proportionate to the number of
individuals in the population.
38. Random sampling means that the individuals
chosen to be in the sample are selected by
chance. Random sampling minimizes the
chance that one part of the population is over-
or underrepresented in the sample. However,
it cannot guarantee that the sample will
accurately represent the population.
39. Answers will vary.
40. Answers will vary.
Section 1.5
1. A closed question is one in which the
respondent must choose from a list of
prescribed responses. An open question is one
in which the respondent is free to choose his
or her own response. Closed questions are
easier to analyze, but limit the responses.
Open questions allow respondents to state
exactly how they feel, but are harder to
analyze due to the variety of answers and
possible misinterpretation of answers.
2. A certain segment of the population is
underrepresented if it is represented in the
sample in a lower proportion than its size in
the population.
3. Bias means that the results of the sample are
not representative of the population. There are
three types of bias: sampling bias, response
bias, and nonresponse bias. Sampling bias is
due to the use of a sample to describe a
population. This includes bias due to
convenience sampling. Response bias
involves intentional or unintentional
misinformation. This would include lying to a
surveyor or entering responses incorrectly.
Nonresponse bias results when individuals
choose not to respond to questions or are
unable to be reached. A census can suffer
from response bias and nonresponse bias, but
would not suffer from sampling bias.
4. Nonsampling error is the error that results
from undercoverage, nonresponse bias,
response bias, or data-entry errors. Essentially,
it is the error that results from the process of
obtaining and recording data. Sampling error
is the error that results because a sample is
being used to estimate information about a
population. Any error that could also occur in
a census is considered a nonsampling error.
5. (a) Sampling bias. The survey suffers from
undercoverage because the first
60 customers are likely not
representative of the entire customer
population.
(b) Since a complete frame is not possible,
systematic random sampling could be
used to make the sample more
representative of the customer population.
6. (a) Sampling bias. The survey suffers from
undercoverage because only homes in the
southwest corner have a chance to be
interviewed. These homes may have
different demographics than those in
other parts of the village.
(b) Assuming that households within any
given neighborhood have similar
household incomes, stratified sampling
might be appropriate, with neighborhoods
as the strata.
7. (a) Response bias. The survey suffers from
response bias because the question is
poorly worded.
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Section 1.5: Bias in Sampling 11
(b) The survey should inform the respondent
of the current penalty for selling a gun
illegally and the question should be
worded as “Do you approve or
disapprove of harsher penalties for
individuals who sell guns illegally?” The
order of “approve” and “disapprove”
should be switched from one individual
to the next.
8. (a) Response bias. The survey suffers from
response bias because the wording of the
question is ambiguous.
(b) The question might be worded more
specifically as “How many hours per
night do you sleep, on average?”
9. (a) Nonresponse bias. Assuming the survey
is written in English, non-English
speaking homes will be unable to read the
survey. This is likely the reason for the
very low response rate.
(b) The survey can be improved by using
face-to-face or phone interviews,
particularly if the interviewers are multi-
lingual.
10. (a) Nonresponse bias
(b) The survey can be improved by using
face-to-face or phone interviews, or
possibly through the use of incentives.
11. (a) The survey suffers from sampling bias
due to undercoverage and interviewer
error. The readers of the magazine may
not be representative of all Australian
women, and advertisements and images
in the magazine could affect the women’s
view of themselves.
(b) A well-designed sampling plan not in a
magazine, such as a cluster sample, could
make the sample more representative of
the population.
12. (a) The survey suffers from sampling bias
due to a bad sampling plan (convenience
sampling) and possible response bias due
to misreported weights on driver’s
licenses.
(b) The teacher could use cluster sampling or
stratified sampling using classes
throughout the day. Each student should
be weighed to get a current and accurate
weight measurement.
13. (a) Response bias due to a poorly worded
question
(b) The question should be reworded in a
more neutral manner. One possible
phrasing might be “Do you believe that a
marriage can be maintained after an
extramarital relation?”
14. (a) Sampling bias. The frame is not
necessarily representative of all college
professors.
(b) To remedy this problem, the publisher
could use cluster sampling and obtain a
list of faculty from the human resources
departments at selected colleges.
15. (a) Response bias. Students are unlikely to
give honest answers if their teacher is
administering the survey.
(b) An impartial party should administer the
survey in order to increase the rate of
truthful responses.
16. (a) Response bias. Residents are unlikely to
give honest answers to uniformed police
officers if their answer would be seen as
negative by the police.
(b) An impartial party should administer the
survey in order to increase the rate of
truthful responses.
17. No. The survey still suffers from sampling
bias due to undercoverage, nonresponse bias,
and potentially response bias.
18. The General Social Survey uses random
sampling to obtain individuals who take the
survey, so the results of their survey are more
likely to be representative of the population.
However, it may suffer from response bias
since the survey is conducted by personal
interview rather than anonymously on the
Internet. The online survey, while potentially
obtaining more honest answers, is basically
self-selected so may not be representative of
the population, particularly if most
respondents are clients of the family and
wellness center seeking help with health or
relationship problems.
19. It is very likely that the order of these two
questions will affect the survey results. To
alleviate the response bias, either question B
could be asked first, or the order of the two
questions could be rotated randomly.
(b) The survey should inform the respondent
of the current penalty for selling a gun
illegally and the question should be
worded as “Do you approve or
disapprove of harsher penalties for
individuals who sell guns illegally?” The
order of “approve” and “disapprove”
should be switched from one individual
to the next.
8. (a) Response bias. The survey suffers from
response bias because the wording of the
question is ambiguous.
(b) The question might be worded more
specifically as “How many hours per
night do you sleep, on average?”
9. (a) Nonresponse bias. Assuming the survey
is written in English, non-English
speaking homes will be unable to read the
survey. This is likely the reason for the
very low response rate.
(b) The survey can be improved by using
face-to-face or phone interviews,
particularly if the interviewers are multi-
lingual.
10. (a) Nonresponse bias
(b) The survey can be improved by using
face-to-face or phone interviews, or
possibly through the use of incentives.
11. (a) The survey suffers from sampling bias
due to undercoverage and interviewer
error. The readers of the magazine may
not be representative of all Australian
women, and advertisements and images
in the magazine could affect the women’s
view of themselves.
(b) A well-designed sampling plan not in a
magazine, such as a cluster sample, could
make the sample more representative of
the population.
12. (a) The survey suffers from sampling bias
due to a bad sampling plan (convenience
sampling) and possible response bias due
to misreported weights on driver’s
licenses.
(b) The teacher could use cluster sampling or
stratified sampling using classes
throughout the day. Each student should
be weighed to get a current and accurate
weight measurement.
13. (a) Response bias due to a poorly worded
question
(b) The question should be reworded in a
more neutral manner. One possible
phrasing might be “Do you believe that a
marriage can be maintained after an
extramarital relation?”
14. (a) Sampling bias. The frame is not
necessarily representative of all college
professors.
(b) To remedy this problem, the publisher
could use cluster sampling and obtain a
list of faculty from the human resources
departments at selected colleges.
15. (a) Response bias. Students are unlikely to
give honest answers if their teacher is
administering the survey.
(b) An impartial party should administer the
survey in order to increase the rate of
truthful responses.
16. (a) Response bias. Residents are unlikely to
give honest answers to uniformed police
officers if their answer would be seen as
negative by the police.
(b) An impartial party should administer the
survey in order to increase the rate of
truthful responses.
17. No. The survey still suffers from sampling
bias due to undercoverage, nonresponse bias,
and potentially response bias.
18. The General Social Survey uses random
sampling to obtain individuals who take the
survey, so the results of their survey are more
likely to be representative of the population.
However, it may suffer from response bias
since the survey is conducted by personal
interview rather than anonymously on the
Internet. The online survey, while potentially
obtaining more honest answers, is basically
self-selected so may not be representative of
the population, particularly if most
respondents are clients of the family and
wellness center seeking help with health or
relationship problems.
19. It is very likely that the order of these two
questions will affect the survey results. To
alleviate the response bias, either question B
could be asked first, or the order of the two
questions could be rotated randomly.
Loading page 15...
12 Chapter 1: Data Collection
20. It is very likely that the order of these two
questions will affect the survey results. To
alleviate the response bias, the order of the
two questions could be rotated randomly.
Prohibit is a strong word. People generally do
not like to be prohibited from doing things. If
the word must be used, it should be offset by
the word “allow.” The use of the words
“prohibit” and “allow” should be rotated
within the question.
21. The company is using a reward in the form of
the $5.00 payment and an incentive by telling
the reader that his or her input will make a
difference.
22. The two choices need to be rotated so that any
response bias due to the ordering of the
questions is minimized.
23. For random digit dialing, the frame is anyone
with a phone (whose number is not on a do-
not-call registry). Even those with unlisted
numbers can still be reached through this
method.
Any household without a phone, households
on the do-not-call registry, and homeless
individuals are excluded. This could result in
sampling bias due to undercoverage if the
excluded individuals differ in some way than
those included in the frame.
24. Answers will vary. The use of caller ID has
likely increased nonresponse bias of phone
surveys since individuals may not answer calls
from numbers they do not recognize. If
individuals with caller ID differ in some way
from individuals without caller ID, then phone
surveys could also suffer from sampling bias
due to undercoverage.
25. It is extremely likely, particularly if
households on the do-not-call registry have a
trait that is not part of those households that
are not on the registry.
26. There is a higher chance that an individual at
least 70 years of age will be at home when an
interviewer makes contact.
27. Some nonsampling errors presented in the
article as leading to incorrect exit polls were
poorly trained interviewers, interviewer bias,
and over representation of female voters.
28. – 32. Answers will vary.
33. The Literary Digest made an incorrect
prediction due to sampling bias (an incorrect
frame led to undercoverage) and nonresponse
bias (due to the low response rate).
34. Answers will vary. (Gallup incorrectly
predicted the outcome of the 1948 election
because he quit polling weeks before the
election and missed a large number of
changing opinions.)
35. (a) Answers will vary. Stratified sampling
by political affiliation (Democrat,
Republican, etc.) could be used to ensure
that all affiliations are represented. One
question that could be asked is whether or
not the person plans to vote in the next
election. This would help determine
which registered voters are likely to vote.
(b) Answers will vary. Possible explanations
are that presidential election cycles get
more news coverage or perhaps people
are more interested in voting when they
can vote for a president as well as a
senator. During non-presidential cycles it
is very informative to poll likely
registered voters.
(c) Answers will vary. A higher percentage
of Democrats in polls versus turnout will
lead to overstating the predicted
Democrat percentage of Democratic
votes.
36. It is difficult for a frame to be completely
accurate since populations tend to change over
time and there can be a delay in identifying
individuals who have joined or left the
population.
37. Nonresponse can be addressed by conducting
callbacks or offering rewards.
38. Trained, skillful interviewers can elicit
responses from individuals and help them give
truthful responses.
39. Conducting a presurvey with open questions
allows the researchers to use the most popular
answers as choices on closed-question
surveys.
40. Answers will vary. Phone surveys conducted
in the evening may result in reaching more
potential respondents; however some of these
individuals could be upset by the intrusion.
20. It is very likely that the order of these two
questions will affect the survey results. To
alleviate the response bias, the order of the
two questions could be rotated randomly.
Prohibit is a strong word. People generally do
not like to be prohibited from doing things. If
the word must be used, it should be offset by
the word “allow.” The use of the words
“prohibit” and “allow” should be rotated
within the question.
21. The company is using a reward in the form of
the $5.00 payment and an incentive by telling
the reader that his or her input will make a
difference.
22. The two choices need to be rotated so that any
response bias due to the ordering of the
questions is minimized.
23. For random digit dialing, the frame is anyone
with a phone (whose number is not on a do-
not-call registry). Even those with unlisted
numbers can still be reached through this
method.
Any household without a phone, households
on the do-not-call registry, and homeless
individuals are excluded. This could result in
sampling bias due to undercoverage if the
excluded individuals differ in some way than
those included in the frame.
24. Answers will vary. The use of caller ID has
likely increased nonresponse bias of phone
surveys since individuals may not answer calls
from numbers they do not recognize. If
individuals with caller ID differ in some way
from individuals without caller ID, then phone
surveys could also suffer from sampling bias
due to undercoverage.
25. It is extremely likely, particularly if
households on the do-not-call registry have a
trait that is not part of those households that
are not on the registry.
26. There is a higher chance that an individual at
least 70 years of age will be at home when an
interviewer makes contact.
27. Some nonsampling errors presented in the
article as leading to incorrect exit polls were
poorly trained interviewers, interviewer bias,
and over representation of female voters.
28. – 32. Answers will vary.
33. The Literary Digest made an incorrect
prediction due to sampling bias (an incorrect
frame led to undercoverage) and nonresponse
bias (due to the low response rate).
34. Answers will vary. (Gallup incorrectly
predicted the outcome of the 1948 election
because he quit polling weeks before the
election and missed a large number of
changing opinions.)
35. (a) Answers will vary. Stratified sampling
by political affiliation (Democrat,
Republican, etc.) could be used to ensure
that all affiliations are represented. One
question that could be asked is whether or
not the person plans to vote in the next
election. This would help determine
which registered voters are likely to vote.
(b) Answers will vary. Possible explanations
are that presidential election cycles get
more news coverage or perhaps people
are more interested in voting when they
can vote for a president as well as a
senator. During non-presidential cycles it
is very informative to poll likely
registered voters.
(c) Answers will vary. A higher percentage
of Democrats in polls versus turnout will
lead to overstating the predicted
Democrat percentage of Democratic
votes.
36. It is difficult for a frame to be completely
accurate since populations tend to change over
time and there can be a delay in identifying
individuals who have joined or left the
population.
37. Nonresponse can be addressed by conducting
callbacks or offering rewards.
38. Trained, skillful interviewers can elicit
responses from individuals and help them give
truthful responses.
39. Conducting a presurvey with open questions
allows the researchers to use the most popular
answers as choices on closed-question
surveys.
40. Answers will vary. Phone surveys conducted
in the evening may result in reaching more
potential respondents; however some of these
individuals could be upset by the intrusion.
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