Solution Manual for Fundamentals of Statistics, 6th Edition

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’S
SOLUTIONS MANUAL
DIACRITECH
FUNDAMENTALS OF STATISTICS:
INFORMED DECISIONS
USING DATA
SIXTH 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 ......................................................................................... 4
1.3 Simple Random Sampling .................................................................................................................................. 7
1.4 Other Effective Sampling Methods .................................................................................................................... 9
1.5 Bias in Sampling ............................................................................................................................................... 11
1.6 The Design of Experiments .............................................................................................................................. 14
Chapter 1 Review Exercises ........................................................................................................................................ 21
Chapter 1 Test ............................................................................................................................................................. 24
Case Study: Chrysalises for Cash ................................................................................................................................ 26
Chapter 2 Summarizing Data in Tables and Graphs
2.1 Organizing Qualitative Data ............................................................................................................................. 28
2.2 Organizing Quantitative Data ........................................................................................................................... 38
2.3 Graphical Misrepresentations of Data .............................................................................................................. 51
Chapter 2 Review Exercises ........................................................................................................................................ 53
Chapter 2 Test ............................................................................................................................................................. 58
Case Study: The Day the Sky Roared.......................................................................................................................... 62
Chapter 3 Numerically Summarizing Data
3.1 Measures of Central Tendency ......................................................................................................................... 65
3.2 Measures of Dispersion .................................................................................................................................... 72
3.3 Measures of Central Tendency and Dispersion from Grouped Data ................................................................ 89
3.4 Measures of Position and Outliers .................................................................................................................... 99
3.5 The Five-Number Summary and Boxplots ..................................................................................................... 106
Chapter 3 Review Exercises ...................................................................................................................................... 117
Chapter 3 Test ........................................................................................................................................................... 123
Case Study: Who Was “A Mourner”? ....................................................................................................................... 126
Chapter 4 Describing the Relation between Two Variables
4.1 Scatter Diagrams and Correlation ................................................................................................................... 128
4.2 Least-Squares Regression ............................................................................................................................... 149
4.3 The Coefficient of Determination ................................................................................................................... 161
4.4 Contingency Tables and Association .............................................................................................................. 165
Chapter 4 Review Exercises ...................................................................................................................................... 178
Chapter 4 Test ........................................................................................................................................................... 184
Case Study: Thomas Malthus, Population, and Subsistence ..................................................................................... 187
Chapter 5 Probability
5.1 Probability Rules ............................................................................................................................................ 189
5.2 The Addition Rule and Complements............................................................................................................. 198
5.3 Independence and the Multiplication Rule ..................................................................................................... 206
5.4 Conditional Probability and the General Multiplication Rule ........................................................................ 210
5.5 Counting Techniques ...................................................................................................................................... 217
5.6 Simulating Probability Experiments ............................................................................................................... 221
5.7 Putting It Together: Which Method Do I Use? ............................................................................................... 223
Chapter 5 Review Exercises ...................................................................................................................................... 226
Chapter 5 Test ........................................................................................................................................................... 229
Case Study: The Case of the Body in the Bag ........................................................................................................... 230

Chapter 6 Discrete Probability Distributions
6.1 Discrete Random Variables............................................................................................................................. 233
6.2 The Binomial Probability Distribution ............................................................................................................ 243
Chapter 6 Review Exercises ...................................................................................................................................... 258
Chapter 6 Test ............................................................................................................................................................ 261
Case Study: The Voyage of the St. Andrew .............................................................................................................. 264
Chapter 7 The Normal Probability Distribution
7.1 Properties of the Normal Distribution ............................................................................................................. 266
7.2 Applications of the Normal Distribution ......................................................................................................... 269
7.3 Assessing Normality ....................................................................................................................................... 289
7.4 The Normal Approximation to the Binomial Probability Distribution ........................................................... 292
Chapter 7 Review Exercises ...................................................................................................................................... 296
Chapter 7 Test ............................................................................................................................................................ 301
Case Study: A Tale of Blood Chemistry.................................................................................................................... 304
Chapter 8 Sampling Distributions
8.1 Distribution of the Sample Mean .................................................................................................................... 306
8.2 Distribution of the Sample Proportion ............................................................................................................ 319
Chapter 8 Review Exercises ...................................................................................................................................... 325
Chapter 8 Test ............................................................................................................................................................ 328
Case Study: Sampling Distribution of the Median .................................................................................................... 330
Chapter 9 Estimating the Value of a Parameter Using Confidence Intervals
9.1 Estimating a Population Proportion ................................................................................................................ 336
9.2 Estimating a Population Mean ........................................................................................................................ 343
9.3 Putting It Together: Which Method Do I Use? ............................................................................................... 353
9.4 Estimating a Population Standard Deviation................................................................................................... 359
9.5 Estimating with Bootstrapping ........................................................................................................................ 361
Chapter 9 Review Exercises ...................................................................................................................................... 366
Chapter 9 Test ............................................................................................................................................................ 370
Case Study: Fire-Safe Cigarettes ............................................................................................................................... 372
Chapter 10 Hypothesis Tests Regarding a Parameter
10.1 The Language of Hypothesis Testing.............................................................................................................. 374
10.2 Hypothesis Tests for a Population Proportion................................................................................................. 377
10.2A Using Simulation to Perform Hypothesis Tests on a Population Proportion .................................................. 388
10.2B Hypothesis Tests for a Population Proportion Using the Normal Model ........................................................ 398
10.3 Hypothesis Tests for a Population Mean......................................................................................................... 408
10.3A Using Simulation and the Bootstrap to Perform Hypothesis Tests on a Population Mean ............................. 419
10.4 Putting It Together: Which Method Do I Use? ............................................................................................... 426
10.5 Hypothesis Tests for a Population Standard Deviation ................................................................................... 430
Chapter 10 Review Exercises .................................................................................................................................... 434
Chapter 10 Test .......................................................................................................................................................... 438
Case Study: How Old Is Stonehenge? ....................................................................................................................... 439

Chapter 11 Inference on Two Population Parameters
11.1 Inference about Two Population Proportions ................................................................................................. 442
11.1A Using Randomization Techniques to Compare Two Proportions ................................................................... 457
11.2 Inference about Two Means: Dependent Samples .......................................................................................... 465
11.2A Using Bootstrapping to Conduct Inference on Two Dependent Means.......................................................... 477
11.3 Inference about Two Means: Independent Samples ....................................................................................... 484
11.3A Using Randomization Techniques to Compare Two Independent Means ...................................................... 498
11.4 Putting It Together: Which Method Do I Use? ............................................................................................... 502
11.5 Inference about Two Populations Standard Deviations .................................................................................. 515
Chapter 11 Review Exercises .................................................................................................................................... 520
Chapter 11 Test ......................................................................................................................................................... 525
Case Study: Control in the Design of an Experiment ................................................................................................ 531
Chapter 12 Additional Inferential Methods
12.1 Goodness-of-Fit Test ...................................................................................................................................... 533
12.2 Tests for Independence and the Homogeneity of Proportions ........................................................................ 544
12.3 Testing the Significance of the Least-Squares Regression Model .................................................................. 566
12.3A Using Randomization Techniques on the Slope of the Least-Squares Regression Line ................................. 571
12.4 Confidence and Prediction Intervals ............................................................................................................... 577
Chapter 12 Review Exercises .................................................................................................................................... 583
Chapter 12 Test ......................................................................................................................................................... 590
Case Study: Feeling Lucky? Well, Are You? ............................................................................................................ 597
Appendix B
B.1 Lines ............................................................................................................................................................... 600
B.2 Inference about Two Population Proportions: Dependent Samples................................................................ 608
B.3 Comparing Three or More Means (One-Way Analysis of Variance) ............................................................ 611

Chapter 1
Data Collection
Section 1.1
1. (a) III. Statistics is the science of collecting,
organizing, summarizing, and analyzing
information in order to draw conclusions
and answer questions. It is also about
providing a measure of confidence in any
conclusions.
(b) VIII. The population is the entire group of
individuals to be studied.
(c) IV. The sample is a subset of the group of
individuals that is being studied.
(d) VII. The parameter is a numerical
summary of a population.
(e) I. The statistic is the numerical summary
of a sample.
(f) VI. The individual is a person or object
that is a member of the group being
studied.
(g) II. Descriptive statistics involves
organizing and summarizing data through
tables, graphs, and numerical summaries.
(h) V. Inferential statistics uses methods that
take results from a sample and extends
them to the population, and measures the
reliability of the result.
2. (a) V. A discrete variable has either a finite
number of possible values or countable
number of possible values. The values of
these variables typically result from
counting.
(b) IV. Data are information that describe
characteristics of an individual.
(c) VI. A continuous variable has an infinite
number of possible values that are not
countable. The values of these variables
typically result from measurement.
(d) II. A qualitative variable allows for
classification of individuals based on
some attribute or characteristic.
(e) I. A quantitative variable provides
numerical measures of individuals. The
measures can be added or subtracted, and
provide meaningful results.
(f) III. A variable is the characteristics of the
individuals within the population.
3. 18% is a parameter because it describes a
population (all of the governors).
4. 72% is a parameter because it describes a
population (the entire class).
5. 32% is a statistic because it describes a sample
(the high school students surveyed).
6. 13.3% is a statistic because it describes a
sample (the 12th graders surveyed).
7. 0.366 is a parameter because it describes a
population (all of Ty Cobb’s at-bats).
8. 43.92 hours is a parameter because it describes
a population (all the men who have walked on
the moon).
9. 23% is a statistic because it describes a sample
(the 6076 adults studied).
10. 44% is a statistic because it describes a sample
(the 100 adults interviewed).
11. Qualitative 12. Quantitative
13. Quantitative 14. Qualitative
15. Quantitative 16. Quantitative
17. Qualitative 18. Qualitative
19. Discrete 20. Continuous
21. Continuous 22. Discrete
23. Continuous 24. Continuous
25. Discrete 26. Continuous
27. Nominal 28. Ordinal
29. Ratio 30. Interval
31. Ordinal 32. Nominal
33. Ratio 34. Interval
35. 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.

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2 Chapter 1: Data Collection
36. 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.
37. 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.
38. 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.
39. 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.
40. 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.
41. 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.)
42. 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, 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.
43. (a) The research objective is to determine if
adolescents 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.
44. (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.
45. (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 many
Americans believe the federal
government wastes much of the money
collected in taxes.

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Section 1.1: Introduction to the Practice of Statistics 3
46. (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 1016 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.
47. (a) State is a qualitative variable because it is
an individual categorization.
(b) F scale is a qualitative variable because
each tornado is rated according to a
category.
(c) Fatalities is a quantitative variable
because it is a numerical measure. It is a
discrete variable because it is countable.
(d) Length is a quantitative variable because
it is a numerical measure. It is a
continuous variable because it results
from measurement.
48. (a) State is a variable measured at the
nominal level because values of the
variable name, label, or categorize. In
addition, the naming scheme does not
allow for the values of the variable to be
arranged in a ranked or specific order.
(b) F scale is a variable measured at the
ordinal level because the naming scheme
allows for the values of the variable to be
arranged in a ranked or specific order.
(c) Fatalities is a variable measured at the
ratio level because the ratio of two values
makes sense and a value of zero has
meaning.
(d) Length is a variable measured at the ratio
level because the ratio of two values
makes sense and a value of zero has
meaning.
49. 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.
50. (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.
51. (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.
52. The population is the group to be studied as
defined by the research objective. A sample is
any subset of the population.
53. 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.
The values of a discrete random variable result
from counting. The values of a continuous
random variable result from a measurement.
54. 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.)

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4 Chapter 1: Data Collection
55. 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.
56. 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.
57. 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. (a) III. A designed experiment is when a
researcher randomly assigns the
individuals in a study to groups,
intentionally manipulates the value of an
explanatory variable, controls other
explanatory variables at fixed values, and
then records the value of the response
variable for each individual.
(b) V. An observational study is when a
researcher measures the value of the
response variable without attempting to
influence the value of either the response
or explanatory variables. That is, the
researcher observes the behavior of
individuals in the study and records the
values of the explanatory and response
variables.
(c) IV. A lurking variable is an explanatory
variable that was not considered in a
study, but that affects the value of the
response variable in the study. In addition,
this variable is typically related to other
explanatory variables in the study.
(d) I. Confounding occurs when the effects of
two or more explanatory variables are not
separated. Therefore, any relation that
may exist between an explanatory
variable and the response variable may be
due to some other variable not accounted
for in the study.
(e) II. 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.
3. (a) II. A cohort study follows a group of
individuals over a long period of time.
Characteristics of the individuals are
recorded and some individuals will be
exposed to certain factors (not
intentionally) and others will not. Because
the data are collected over time, cohort
studies are prospective.
(b) III. A cross-sectional study collects
information about individuals at a specific
point in time, or over a short period of
time.
(c) I. A case-control study is retrospective,
meaning it requires the researcher to look
at existing records, or the subject to recall
information from the past. Individuals
who have certain characteristics are
matched with those who don’t.
4. 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.
5. 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.

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Section 1.2: Observational Studies vs. Designed Experiments 5
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.
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.

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6 Chapter 1: Data Collection
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
qualitative.
22. (a) The explanatory variable is web page
design; qualitative
(b) The response variables are time on site
and amount spent. Both are qualitative.
(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) This is a cohort study because a group of
individuals was identified to participate
in the study, and then they were observed
over a period of time.
(b) Because there is a link established
between obesity and cell phone use, and a
link between obesity and negative health
outcomes, if it is determined that cell-
phone users are experiencing higher
incidence rates of negative health
outcomes, it cannot be established that
the factor leading to the negative health
outcome is due to the cell phone—it may
be due to the lurking variable obesity.
25. Because individuals in the early 1900s were
pressured to become right-handed, we would
see a lower proportion of left-handers who are
older in the study. This would make it seem as
though left-handers die younger because the
older individuals in the study are primarily
right-handed.
26. (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.
(c) The response variable is whether the
individual has lung cancer or not. This is
a qualitative variable.

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Section 1.3: Simple Random Sampling 7
(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.
27. Web scraping can be used to extract data from
tables on web pages and then upload the data
to a file. Web scraping can also be used to
create a data set of words from an online
article (that is, fetching unstructured
information and transforming it into a
structured format through something called
parsing and reformatting processes). In
addition, web scraping can be used to
dynamically call information from websites
with links.
28. Answers will vary. Discussions may include
the responsibility of host sites to protect
private information; the ethics behind using
information collected from a site to harm a
competitor; the ethics behind putting stress on
a host’s servers so that the website slows
down; the role of social media to scrape its
site for “fake news.”
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.

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8 Chapter 1: Data Collection
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.
(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, and 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, Reagan, Madison, Trump,
Pierce, Buchanan, Carter, G. W. Bush.
(b) Repeating part (a) with a seed of 99, our
sample would be Nixon, Eisenhower,
Pierce, Arthur, Trump, Hayes, Clinton,
T. Roosevelt.

Loading page 13...

Section 1.4: Other Effective Sampling Methods 9
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.
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.
17. Answers will vary.
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 8th 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.

Loading page 14...

110 Chapte
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Loading page 15...

Section 1.5: Bias in Sampling 11
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.
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. (a) III. Bias occurs when the results of the
sample are not representative of the
population.
(b) I. Sampling bias occurs when the
techniques used to select individuals for a
sample favor one part of the population
over another.
(c) IV. Nonresponse bias occurs when the
individuals selected to be in the sample
who do not respond to the survey have
different opinions from those who do
respond.
(d) II. Response bias occurs when the
answers on a survey do not reflect the true
feelings of the respondent.
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.

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