Solution Manual For Elementary Statistics, 3rd Edition

Name: Solution Manual For Elementary Statistics, 3rd Edition
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Author: Jackson Roberts

Unlock the answers to every textbook problem with Solution Manual For Elementary Statistics, 3rd Edition, making studying more efficient and effective.

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iii
Contents
Chapter 1 Basic Ideas 1
Chapter 2 Graphical Summaries of Data 8
Chapter 3 Numerical Summaries of Data
Chapter 4 Summarizing Bivariate Data 79
Chapter 5 Probability 97
Chapter 6 Discrete Probability Distributions 111
Chapter 7 The Normal Distribution 129
Chapter 8 Confidence Intervals 159
Chapter 9 Hypothesis Testing 179
Chapter 10 Two-Sample Confidence Intervals 207
Chapter 11 Two-Sample Hypothesis Tests 226
Chapter 12 Tests with Qualitative Data 243
Chapter 13 Inference in Linear Models 258
Chapter 14 Analysis of Variance 284
Chapter 15 Nonparametric Statistics 302
42

Chapter 1: Basic Ideas
Section 1.1
Exercises 1 – 6 are the Check Your
Understanding exercises for this section.
Answers to these exercises are on page 12
of the text book.
Understanding the Concepts
7. population
8. sample
9. simple random sample
10. sample of convenience
11. cluster
12. stratified
13. False. In some cases it is difficult or
impossible to draw a sample in a truly
random way. In these cases, the best one
can do is to sample items by some
convenient method. A sample of
convenience is one way.
14. False. In a stratified sample, the
population is divided into groups, and a
random sample from each group is drawn.
15. True
16. True
Practicing the Skills
17. Statistic
18. Parameter
19. Parameter
20. Statistic
21. Answers will vary.
22. Answers will vary. Stratified sample
23. Answers will vary. Cluster sample
24. Answers will vary. Systematic sample
25. Stratified sample
26. Sample of convenience
27. Cluster sample
28. Systematic sample
29. Voluntary response sample
30. Cluster sample
31. Sample of convenience
32. Simple random sample
33. Stratified sample
34. Cluster sample
35. Simple random sample
36. Stratified sample
37. Systematic sample
38. Voluntary response sample
Working with the Concepts
39. It will be necessary to draw a sample of
convenience. There is no list of all
headache sufferers from which to draw a
simple random sample.
40. It is feasible to draw a simple random
sample of students from a list of all
students enrolled.
41. Answers will vary. A simple random
sample could be drawn from a list of all
registered voters in the town.
42. Answers will vary. A systematic sample
could be used in which every tenth item
was sampled.
43. Answers will vary. A stratified sample,
consisting of simple random samples of
100 men and 100 women, could be drawn.
44. Answers will vary. A simple random
sample of tax forms could be drawn.
Extending the Concepts
45. Answers will vary.

46. Let’s say we will sample every kth item.
This determines k − 1 clusters; the first
cluster consists of items 1, k + 1, 2k + 1, …;
the second cluster consists of items 2, k +
2, 2k + 2, …; and so on. Choosing a
systematic sample is like choosing one of
these clusters at random.
Section 1.2
Exercises 1 – 4 are the Check Your
Understanding exercises for this section.
Answers to these exercises are on page 18.
Understanding the Concepts
5. variables
6. qualitative
7. Quantitative
8. nominal; ordinal
9. discrete
10. Continuous
11. False. Quantitative variables describe how
much or how many of something there is.
12. True
13. True
14. True
Practicing the Skills
15. Qualitative
16. Quantitative
17. Quantitative
18. Qualitative
19. Quantitative
20. Quantitative
21. Qualitative
22. Qualitative
23. Qualitative
24. Quantitative
25. Ordinal
26. Nominal
27. Ordinal
28. Ordinal
29. Nominal
30. Nominal
31. Nominal
32. Ordinal
33. Continuous
34. Continuous
35. Discrete
36. Discrete
37. Continuous
38. Discrete
39. Discrete
40. Continuous
Working with the Concepts
41. Ordinal
42. Discrete
43. Ordinal
44. Quantitative
45. Nominal
46. Ordinal
47. (A) Game Title, System
(B) Release Year, Copies Sold
(C) System
(D) Game Title
48. (A) Movie Title, Genre
(B) Release Year, Ticket Sales, Running
Time
(C) Genre
(D) Movie Title

Extending the Concepts
49. (A) Ordinal
(B) Yes, it reflects a more favorable
opinion of the construction of a new
shopping mall.
(C) No, we cannot say that Jason’s
opinion is twice as favorable.
(D) Quantitative
(E) Yes, Brenda’s answer reflects the
ownership of more cars, and
specifically, the ownership of twice as
many cars.
(F) Nominal
(G) No, Brenda’s answer reflects neither
more of something nor twice as much
of something.
Section 1.3
Exercises 1 – 4 are the Check Your
Understanding exercises for this section.
Answers to these exercises are on page 26.
Understanding the Concepts
5. randomized
6. double-blind
7. observational
8. confounder
9. prospective
10. cohort
11. True
12. False. A confounder makes it harder to
draw conclusions from a study.
13. False. In a randomized experiment,
subjects are assigned to treatment groups
at random.
14. False. Randomized experiments are
generally more reliable than observational
studies.
15. True
16. True
Practicing the Skills
17. (A) Randomized experiment
(B) Yes, because the assignment to
treatments is made at random, there is
no systematic difference between the
groups other than the drug taken that
can explain the difference in pain
relief.
18. (A) Observational study
(B) No, because this is an observational
study, the results may be due to
confounding. For example, those in
the low-exercise group may be older
and have higher blood pressure as a
result of age.
19. (A) Randomized experiment
(B) Yes, because the assignment to
treatments is made at random, there is
no systematic difference between the
groups other than the amount of
exercise that can explain the
difference in blood pressure.
20. (A) The four types of fertilizer
(B ) Randomized experiment
(C) Yes, because the assignment to
treatment is made at random.

Working with the Concepts
21. An observational study will be necessary,
because one can’t assign people to live in
areas with high pollution levels.
22. A randomized experiment is possible, with
cold sufferers being assigned randomly to
the old or new drug.
23. The result may be due to confounding.
Areas with denser populations may have
both more crime and more taxicabs.
24. The result could be due to confounding.
For example, more older people may live
in larger houses than younger people, and
also have less chance of recovering from a
heart attack.
25. (A) False
(B) True
26. Children with larger vocabularies tend to
be older, and thus taller.
27. (A) Heart rate
(B) Maternal smoking
(C) Cohort
(D) Prospective
(E) Yes. The level of prenatal care may
differ between smoking and
nonsmoking mothers.
28. (A) Whether respiratory problems were
experienced
(B) The level of formaldehyde in the
classroom
(C) A cohort study
(D) Cross-sectional
(E) It is unlikely. For confounding to be
an issue, children with more sensitive
respiratory systems would have to
have been more likely to be assigned
to classrooms with higher exposure.
Extending the Concepts
29. (A) Yes, because the subjects were
randomly assigned to treatment.
(B) If a doctor knew whether a child had
received the vaccine, it might
influence the diagnosis.
(C) It could be due to confounding. The
children who received the placebo
were more likely to be middle- or
upper-income than those who did not
participate, and this may be the reason
that the rate of polio was higher.
30. (A) No
(B) No
(C) The treatment group consisted of
children who had consent to
participate; middle- and upper-income
children were overrepresented in this
group. Therefore, the children in the
treatment group tended to be more
susceptible to polio than those in the
control group.
31. Smokers who quit are less healthy than
smokers who don’t. Upon quitting
smoking, many people put on weight
substituting food for tobacco.
32. Smokers tend to drink more alcohol on
the average than non-smokers.
Section 1.4
Exercises 1 and 2 are the Check Your
Understanding exercises for this section.
Answers to these exercises are on page 30.

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Understanding the Concepts
3. Voluntary response surveys
4. nonresponders
5. population
6. False. The way that a question is worded
in a survey may have a large effect on the
responses.
7. True
8. False. A large sample size does not make
up for bias in questioning.
Practicing the Skills
9. Nonresponse bias
10. Voluntary response bias
11. Self-interest bias
12. Self-interest bias
13. Voluntary response bias
14. Social acceptability bias
15. Nonresponse bias
16. Social acceptability bias
Working with the Concepts
17. (A) No
(B) No. Both questions are leading. The
first question leads to a ‘‘yes’’
response, and the second leads to a
‘‘no’’ response.
18. Yes. People may be less likely to answer
the phone when they don’t recognize the
number that is calling them.
19. Yes. People who do not have landline
phones may tend to have different
opinions on some issues than people who
do have landline phones.
20. Yes, people may be more likely to pick the
first choice.
Extending the Concepts
21. (A) The poll oversampled higher-income
people.
(B) The response rate was low — only
23%. This results in nonresponse bias.
(C) A sample that is not drawn by a valid
method can produce misleading
results, even when it is large.
CHAPTER 1 Quiz
1. Answers will vary.
2. Qualitative
3. True
4. Continuous
5. False. Ideally a sample should represent
the population as much as possible.
6. Stratified sample
7. acceptable
8. Sample of convenience
9. True
10. Observational study
11. Randomized experiment
12. differences in treatment
13. Seniors may be more likely to have better
preparation for the class than sophomores.
14. True
15. Not reliable. This is a voluntary response
survey, so the people who respond tend to
hold stronger opinions than others.
CHAPTER 1 Review Exercises
1. Quantitative
2. Nominal

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3. Continuous
4. (A) True
(B) True
(C) False
5. Stratified sample
6. Voluntary response sample
7. Cluster sample
8. Simple random sample
9. (A) Observational study
(B) Yes. People who live in areas with
fluoridated water may have different
dental habits than those who live in
areas without fluoridated water.
10. (A) Randomized experiment
(B) Because this is a randomized
experiment, the results are unlikely to
be due to confounding.
11. (A) Observational study
(B) Yes. People who talk on cell phones
while driving may be more careless in
general than those who do not.
12. (A) Randomized experiment
(B) Because this is a randomized
experiment, the results are unlikely to
be due to confounding.
13. The sample is a voluntary response
sample.
14. Nonresponse bias; living people are not
included. People who are still alive are not
included in the sample.
15. There is a considerable level of
nonresponse bias.
Write About It
1. In both cluster sampling and stratified
sampling, the population is divided into
groups. In stratified sampling, a simple
random sample is chosen from each
group. In cluster sampling, a random
sample of groups is chosen, and every
member of the chosen groups is sampled.
2. A potential problem with samples of
convenience is that they may differ
systematically in some way from the
population. For this reason, samples of
convenience should not be used, except in
situations where it is not feasible to draw a
random sample. When it is necessary to
draw a sample of convenience, it is
important to think carefully about all the
ways in which the sample might differ
systematically from the population. If it is
reasonable to believe that no important
systematic difference exists, then it may be
acceptable to use a sample of convenience.
3. Answer will vary.
4. Answers will vary.
5. Some qualitative variables may be
numeric when the number represents a
label. Examples include numbers on a
football jersey or on a racecar.
6. A randomized experiment is a study in
which the investigator assigns the
treatments to the experimental units at
random. An observational study is one in
which the assignment to treatment groups
is not made by the investigator. The main
advantage to conducting a randomized
experiment is that if there are large
differences in outcomes among the
treatment groups, we may conclude that
the differences are due to the treatments.
7. The main advantage to conducting a
double-blind study is that it is an impartial
experiment which eliminates the potential

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for bias from the investigator or the
subject. There are various limitations. A
double-blind experiment requires a third
party to be involved in the experiment.
Also, there may be factors that may
influence the outcome that are not known
when the experiment is double-blinded.
8. Answers will vary.
9. (A) This is an example of leading question
bias. It highly encourages a “yes” response
because of the phrase “or continue their
wasteful spending.” A more appropriate
question would be “What is your opinion
of Americans saving more money?
Choices: Strongly disagree, Somewhat
disagree, Neither agree nor disagree,
Somewhat agree, Strongly agree.’’
(B) This is an example of leading question
bias. It highly encourages a “yes” response
because of the word “reputable.” A more
appropriate question would be “What is
your opinion of the current level of
funding for charities?”
CHAPTER 1 Case Study
1. 450
2. 41
3. 41
450 = 9.1%
4. 43
5. 2
6. 2
43 = 4.7%
7. Yes, 9.1% is considerably larger than 4.7%.
8. The high-exposure people and the school-
return people are the same people.
9. The low-exposure people and the mail-
return people are the same people.
10. People who respond by mail will be
responding during a period of lower PM.
11. People with symptoms may tend to
respond earlier; therefore, people with
symptoms are more likely to be school-
return people.
12. There would be no tendency for people
with symptoms to respond earlier.

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Chapter 2: Graphical Summaries of Data
Section 2.1 Exercises
Exercises 1 – 4 are the Check Your
Understanding exercises located within
the section. Their answers are found on
pages 48 and 49.
Understanding the Concepts
5. frequency
6. relative frequency
7. Pareto chart
8. pie chart
9. False. In a frequency distribution, the sum
of all frequencies equals the total number
of observations.
10. True
11. True
12. False. In bar graphs and Pareto charts, the
heights of the bars represent the
frequencies or relative frequencies.
Practicing the Skills
13. (A) Meat, poultry, fish, and eggs
(B) False ($450 < $550)
(C) True ($1300 > $1000)
14. (A) Type O
(B) False ( 70 46.7%
150 = )
(C) True
15. (A)
(B)
(C) Everyone (E)
(D) False
(E) True (12.5% < 20%)
16. (A)
(B)
(C) Medicare and Medicaid
(D) 68.8% (27.7% + 25.1% + 9.6% +
6.4%)
17. (A) West, South
(B) Northeast, Midwest
(C) True
(D) False (the Northeast had around
18%)

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