# Solution Manual for Statistical Methods for the Social Sciences, 5th Edition

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INSTRUCTORโS
SOLUTIONS MANUAL
JAMES LAPP
S TATISTICAL M ETHODS
FOR THE S OCIAL S CIENCES
FIFTH EDITION
Alan Agresti
University of Florida
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher
make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this
book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with,
or arising out of, the furnishing, performance, or use of these programs.
Reproduced by Pearson from electronic files supplied by the author.
Copyright ยฉ 2018, 2012, 2009 Pearson Education, Inc.
Publishing as Pearson, 330 Hudson Street, NY NY 10013
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form
or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the
publisher. Printed in the United States of America.
ISBN-13: 978-0-13-451277-8
ISBN-10: 0-13-451277-4
CONTENTS
Chapter 1: Introduction ………………………………………………………………………………………….. 1
Chapter 2: Sampling and Measurement…………………………………………………………………….3
Chapter 3: Descriptive Statistics………………………………………………………………………………7
Chapter 4: Probability Distributions ……………………………………………………………………….21
Chapter 5: Statistical Inference: Estimation …………………………………………………………….29
Chapter 6: Statistical Inference: Significance Tests ………………………………………………….37
Chapter 7: Comparison of Two Groups…………………………………………………………………..47
Chapter 8: Analyzing Association Between Categorical Variables …………………………….59
Chapter 9: Linear Regression and Correlation………………………………………………………….67
Chapter 10: Introduction to Multivariate Relationships …………………………………………….83
Chapter 11: Multiple Regression and Correlation …………………………………………………….89
Chapter 12: Regression with Categorical Predictors: Analysis of Variance Methods ….103
Chapter 13: Multiple Regression with Quantitative and Categorical Predictors………….111
Chapter 14: Model Building with Multiple Regression……………………………………………117
Chapter 15: Logistic Regression: Modeling Categorical Responses………………………….127
Chapter 16: An Introduction to Advanced Methodology …………………………………………135
Chapter 1: Introduction 1
Chapter 1: Introduction
1.1.
(a) an individual Prius (automobile)
(b) All Prius automobiles used in the EPA tests.
(c) All Prius automobiles that are or may be manufactured.
1.2.
(a) all 7.3 million voters is the population. The sample is the 1824 voters surveyed.
(b) A statistic is the 60.5% who voted for Brown from the exit poll sample of size 1824; a parameter is the
60.0% who actually voted for Brown.
1.3.
(a) all students at the University of Wisconsin
(b) A statistic, since it’s calculated only for the 100 sampled students.
1.4.
The values are statistics, since they is based on the 1028 adults in the sample.
1.5.
(a) all adult Americans
(b) Proportion of all adult Americans who would answer definitely or probably true.
(c) The sample proportion 0.523 estimates the population proportion.
(d) No, it is a prediction of the population value but will not equal it exactly, because the sample is only a
very small subset of the population.
1.6.
(a) The most common response was 2 hours per day.
(b) This is a descriptive statistic because it describes the results of a sample.
1.7.
(a) A total of 85.7% said โyes, definitelyโ or โyes, probably.โ
(b) In 1998, a total of 85.8% said โyes, definitelyโ or โyes, probably.โ
(c) A total of 74.4% said โyes, definitelyโ or โyes, probably.โ The percentages of yes responses were higher
for HEAVEN than for HELL.
1.8.
(a) Statistics, since they’re based on a sample of 60,000 households, rather than all households.
(b) Inferential, predicting for a population using sample information.
1.9.
The correct answer is (a).
1.10.
Race
white
black
white
Hispanic
white
Age
19
23
38
20
41
Sentence
2
1
10
2
5
Felony?
no
no
yes
no
yes
Prior Arrests
2
0
8
1
5
Prior Convictions
1
0
3
1
4
1.11. (a) There are 60 rows in the data.
(b) Answers will vary.
1.12. Answers will vary.
1.13. Answers will vary.
1.14. (a) A statistic is a numerical summary of the sample data, while a parameter is a numerical summary of the
population. For example, consider an exit poll of voters on election day. The proportion voting for a
particular candidate is a statistic. Once all of the votes have been counted, the proportion of voters who voted
for that candidate would be known (and is the parameter).
(b) Description deals with describing the available data (sample or population), whereas inference deals with
making predictions about a population using information in the sample. For example, consider a sample of
voters on election day. One could use descriptive statistics to describe the voters in terms of gender, race,
party, etc., and inferential statistics to predict the winner of the election.
Copyright ยฉ 2018 Pearson Education, Inc.
2 Statistical Methods for the Social Sciences
1.15. If you have a census, you do not need to use the information from a sample to describe the population since
you have information from the population as a whole.
1.16. (a) The descriptive part of this example is that the average age in the sample is 24.1 years.
(b) The inferential part of this example is that the sociologist estimates the average age of brides at marriage
for the population to between 23.5 and 24.7 years.
(c) The population of interest is women in New England in the early eighteenth century.
1.17. (a) A statistic is the 78% of the sample of subjects interviewed in the UK who said yes.
(b) A parameter is the true percent of the 50 million adults in the UK who would say yes.
(c) A descriptive analysis is that the percentage of yes responses in the survey varied from 56% (in Denmark)
to 95% (in Cyprus).
(d) An inferential analysis is that the percentage of adults in the UK who would say yes falls between 75%
and 81%.
1.18. Answers will vary.
1.19. Answers will vary.
Copyright ยฉ 2018 Pearson Education, Inc.
Chapter 2: Sampling and Measurement 3
Chapter 2: Sampling and Measurement
2.1.
(a) Discrete variables take a finite set of values (or possible all nonnegative integers), and we can enumerate
them all. Continuous variables take an infinite continuum of values.
(b) Categorical variables have a scale that is a set of categories; for quantitative variables, the measurement
scale has numerical values that represent different magnitudes of the variable.
(c) Nominal variables have a scale of unordered categories, whereas ordinal variables have a scale of ordered
categories. The distinctions among types of variables are important in determining the appropriate descriptive
and inferential procedures for a statistical analysis.
2.2.
(a) quantitative
(b) categorical
(c) categorical
(d) quantitative
(e) categorical
(f) quantitative
(g) categorical
(h) quantitative
(i) categorical
2.3.
(a) ordinal
(b) nominal
(c) interval
(d) nominal
(e) nominal
(f) ordinal
(g) interval
(h) ordinal
(i) nominal
(j) interval
(k) ordinal
2.4.
(a) nominal
(b) nominal
(c) ordinal
(d) interval
(e) interval
(f) interval
(g) ordinal
(h) interval
(i) nominal
(j) interval
2.5.
(a) interval
(b) ordinal
(c) nominal
2.6.
(a) state of residence
(b) number of siblings
(c) social class (high, medium, low)
(d) student status (full time, part time)
(e) Number of cars owned.
(f) Time (in minutes) needed to complete an exam.
(g) number of siblings
2.7.
(a) Ordinal, since there is a sense of order to the categories.
(b) discrete
(c) These values are statistics, because they apply to a sample of size 1962, not the entire population.
2.8.
ordinal
2.9.
The correct responses are (b), (c), (d), (e) and (f).
2.10. The correct responses are (a), (c), (e), and (f).
2.11. Answers will vary.
2.12. Number names 00001 to 52000. Answers will vary 6907.
Copyright ยฉ 2018 Pearson Education, Inc.
4 Statistical Methods for the Social Sciences
2.13. (a) observational study
(b) experiment
(c) observational study
(d) experiment
2.14. (a) Experimental study, since the researchers are assigning subjects to treatments.
(b) An observational study could look those who grew up in nonsmoking or smoking environments and
examine incidence of lung cancer.
2.15
(a) Sample-to-sample variability causes the results to vary.
(b) The sampling error for the Gallup poll is โ2.1% for Obama and 2.8% for Romney.
2.16. (a) This is a volunteer sample because viewers chose whether to call in.
(b) The mail-in questionnaire is a volunteer sample because readers chose whether to respond.
2.17. The first question is confusing in its wording. The second question has clearer wording.
2.18. (a) Skip number is k ๏ฝ 52, 000 / 5 ๏ฝ 10, 400. Randomly select one of the first 10,400 names and then skip
10,400 names to get each of the next names. For example, if the first name picked is 01536, the other four
names are 01536 ๏ซ 10400 ๏ฝ 11936, 11936 ๏ซ 10400 ๏ฝ 22336, 22336 ๏ซ 10400 ๏ฝ 32736, 32736 ๏ซ 10400 ๏ฝ 43136.
(b) We could treat the pages as clusters. We would select a random sample of pages, and then sample every
name on the pages selected. Its advantage is that it is much easier to select the sample than it is with random
sampling. A disadvantage is as follows: Suppose there are 100 โMartinezโ listings in the directory, all falling
on the same page. Then with cluster sampling, either all or none of the Martinez families would end up in the
sample. If they are all sampled, certain traits which they might have in common (perhaps, e.g., religious
affiliation) might be over-represented in the sample.
2.19. Draw a systematic sample form the student directory, using skip number k ๏ฝ 5000 100 ๏ฝ 50.
2.20. (a) This is not a simple random sample since the sample will necessarily have 25 blacks and 25whites. A
simple random sample may or may not have exactly 25 blacks and 25 whites.
(b) This is stratified random sampling. You ensure that neither blacks nor whites are over-sampled.
2.21. (a) the clusters
(b) The subjects within every stratum.
(c) The main difference is that a stratified random sample uses every stratum, and we want to compare the
strata. By contrast, we have a sample of clusters, and not all clusters are representedโthe goal is not to
compare the clusters but to use them to obtain a sample.
2.22. (a) Categorical are GE, VE, AB, PI, PA, RE, LD, AA; quantitative are AG, HI, CO, DH, DR, NE, TV, SP,
AH.
(b) Nominal are GE, VE, AB, PA, LD, AA; ordinal are PI and RE; interval are AG, HI, CO, DH, DR, NE,
TV, SP, AH.
2.23. Answers will vary.
2.24. (a) Draw a systematic sample from the student directory, using skip number k ๏ฝ N 100, where N ๏ฝ number
of students on the campus.
(b) High school GPA on a 4-point scale, treated as quantitative, interval, continuous; math and verbal SAT
on a 200 to 800 scale, treated as quantitative, interval, continuous; whether work to support study (yes, no),
treated as categorical, nominal, discrete; time spent studying in average day, on scale (none, less than 2
hours, 2โ4 hours, more than 4 hours), treated as quantitative, ordinal, discrete.
2.25. This is nonprobability sampling; certain segments may be over- or under-represented, depending on where
the interviewer stands, time of day, etc. Quota sampling fails to incorporate randomization into the selection
method.
2.26. Responses can be highly dependent on nonsampling errors such as question wording.
Copyright ยฉ 2018 Pearson Education, Inc.
Chapter 2: Sampling and Measurement 5
2.27. (a) This is a volunteer sample, so results are unreliable; e.g., there is no way of judging how close 93% is to
the actual population who believe that benefits should be reduced.
(b) This is a volunteer sample; perhaps an organization opposing gun control laws has encouraged members
to send letters, resulting in a distorted picture for the congresswoman. The results are completely unreliable
as a guide to views of the overall population. She should take a probability sample of her constituents to get a
less biased reaction to the issue.
(c) The physical science majors who take the course might tend to be different from the entire population of
physical science majors (perhaps more liberal minded on sexual attitudes, for example). Thus, it would be
better to take random samples of students of the two majors from the population of all social science majors
and all physical science majors at the college.
(d) There would probably be a tendency for students within a given class to be more similar than students in
the school as a whole. For example, if the chosen first period class consists of college-bound seniors, the
members of the class will probably tend to be less opposed to the test than would be a class of lower
achievement students planning to terminate their studies with high school. The design could be improved by
taking a simple random sample of students, or a larger random sample of classes with a random sample of
students then being selected from each of those classes (a two-stage random sample).
2.28. A systematic sample with a skip number of 7 (or a multiple of 7) would be problematic since the sampled
editions would all be from the same day of the week (e.g., Friday). The day of the week may be related to the
percentage of newspaper space devoted to news about entertainment.
2.29. Because of skipping names, two subjects listed next to each other on the list cannot both be in the sample, so
not all samples are equally likely.
2.30. If we do not take a disproportional stratified random sample, we might not have enough Native Americans in
our sample to compare their views to those of other Americans.
2.31. If a subject is in one of the clusters that is not chosen, then this subject can never be in the sample. Not all
samples are equally likely.
2.32. Answers will vary
2.33. The nursing homes can be regarded as clusters. A systematic random sample is taken of the clusters, and then
a simple random sample is taken of residents from within the selected clusters.
2.34. The best answer is (b).
2.35. The best answer is (c).
2.36. The best answer is (c).
2.37. The best answer is (a).
2.38. False; this is a convenience sample.
2.39. False; this is a voluntary response sample.
2.40. An annual income of $40,000 is twice the annual income of $20,000. However, 70 degrees Fahrenheit is not
twice as hot as 35 degrees Fahrenheit. (Note that income has a meaningful zero and temperature does not.) IQ is
not a ratio-scale variable.
Copyright ยฉ 2018 Pearson Education, Inc.
Chapter 3: Descriptive Statistics 7
Chapter 3: Descriptive Statistics
3.1.
(a)
Place of Birth
Europe
Asia
Caribbean
Central America
South America
Other
Number (Millions)
4.5
10.1
3.6
14.4
2.4
2.6
Total
Relative Frequency
4.5 / 37.6 ๏ฝ 12.0%
10.1/ 37.6 ๏ฝ 26.9 %
3.6 / 37.6 ๏ฝ 9.6%
14.4 / 37.6 ๏ฝ 38.3%
2.4 / 37.6 ๏ฝ 6.4%
2.6 / 37.6 ๏ฝ 6.9%
37.6
(b)
16
14
Number (M illions)
12
10
8
6
4
2
0
Eur
Asia
Carib
C. Am
S. Am
Other
Place of Birth
(c) โPlace of birthโ is categorical.
(d) The mode is Central America.
3.2.
(a)
Religion
Christianity
Islam
Hinduism
Buddhism
Total
Number (Billions)
2.2
1.6
1.0
0.5
Relative Frequency
2.2 / 5.3 ๏ฝ 41.5%
1.6 / 5.3 ๏ฝ 30.2%
1.0 / 5.3 ๏ฝ 18.9%
0.5 / 5.3 ๏ฝ 9.4%
5.3
Copyright ยฉ 2018 Pearson Education, Inc.
8 Statistical Methods for the Social Sciences
3.2
(continued)
(b)
2.5
Number (Billions)
2.0
1.5
1.0
0.5
0.0
Christianity
Islam
Hinduism Buddhism
Religion
(c) The mean or median cannot be calculated for these data since they are categorical. The mode of these
four religions is Christianity. Christianity is also the mode of all religions.
3.3.
(a) There are 33 students. The minimum score is 65, and the maximum score is 98.
(b)
7
6
Frequency
5
4
3
2
1
0
65
70
75
80
85
90
95
100
M idterm Score
3.4.
(a)
Persons per Household
1
2
3
4
5 or more
Number (Millions)
30.1
37.1
17.8
15.0
10.4
Total
110.4
Copyright ยฉ 2018 Pearson Education, Inc.
Relative Frequency
30.1/110.4 ๏ฝ 27.3%
37.1/110.4 ๏ฝ 33.6%
17.8 /110.4 ๏ฝ 16.1%
15.0 /110.4 ๏ฝ 13.6%
10.4 /110.4 ๏ฝ 9.4%
Chapter 3: Descriptive Statistics 9
3.4
(continued)
(b) The distribution is right skewed.
40
Number (M illions)
30
20
10
0
1
2
3
4
5+
Persons per Household
(c) The median household size is 2 persons, and the mode is also 2 persons.
(a)
Murder Rate
1+
2+
3+
4+
5+
6+
7+
8+
9+
10+
Total
Frequency
7
11
8
7
9
6
1
0
0
1
50
Relative Frequency
14%
22%
16%
14%
18%
12%
2%
0%
0%
2%
(b)
12
Frequency (per 100,000 population)
3.5.
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10 11 12
M urder Rate
The distribution appears to be somewhat skewed right, with outlier at 10.8.
Copyright ยฉ 2018 Pearson Education, Inc.
10 Statistical Methods for the Social Sciences
3.5
(continued)
(c)
Stem (1)
Leaves (0.1)
4567778
00122344899
13348899
2356678
001444568
012445
2
1
2
3
4
5
6
7
8
9
10 8
The stem-and-leaf plot looks like the histogram turned on its side.
3.6.
(a) GDP is rounded to the nearest thousand
Stem (10,000s)
Leaves (1,000s)
1
2
3
4
5
6
7
8
9
9
66
2456678
0033333444
34
5
1
(b)
10
9
8
Frequency
7
6
5
4
3
2
1
0
10 20 30
40 50 60 70
80 90 100
Rounded GDP (thousands)
(c) The outlier in each plot is Luxembourg.
3.7.
(a) The mean is 129.5 and the median is 102
(b) The mean would be higher because of the skew to the right and the extreme outlier (716 for the U.S.)
(c) Without the United States, the mean is 104 and the median is 98. There is a greater effect on mean.
Copyright ยฉ 2018 Pearson Education, Inc.
Chapter 3: Descriptive Statistics 11
3.8.
(a) The mean is ๏จ 0.4 ๏ซ 2.2 ๏ซ 6.2 ๏ซ 1.7 ๏ซ 1.8 ๏ซ 0.9 ๏ซ 12.2 ๏ซ 17.6๏ฉ 8 ๏ฝ 5.375 metric tons per person. The median is
2.0 metric tons per person.
(b) The mean is now ๏จ 0.4 ๏ซ 2.2 ๏ซ 6.2 ๏ซ 1.7 ๏ซ 1.8 ๏ซ 0.9 ๏ซ 12.2 ๏ซ 17.6 ๏ซ 40.3๏ฉ 9 ๏ฝ 9.26 metric tons per person. The
median is 2.2 metric tons per person. Qatar had a greater impact on the mean.
3.9.
(a) The response โnot far enoughโ is the mode.
(b) The median is โnot far enough.โ We cannot the mean with these data since they are categorical.
3.10. (a) For the data from the previous 2, the mean is 16.6 days, the median is 12 days, and the standard deviation
is 13.9. For the data from 25 years ago, the mean was 27.6 days, the median was 24 days, and the standard
deviation is 12.4. The mean has decreased by 11 days, and the median has decreased by 12 days since 25
years ago. The variability in length of stay was slightly lower 25 years ago.
(b) Of the 11 observations, the median is 13 days. We cannot calculate the mean, but substituting 40 for the
censored observation gives a mean of 18.7 days.
3.11. (a)
TV Hours
0
1
2
3
4
5
6
7+
Total
Frequency
120
310
437
293
227
113
75
94
1669
Relative Frequency
7.2
18.6
26.2
17.6
13.6
6.8
4.5
5.6
100.1
(b) The distribution is unimodal and right skewed.
(c) The median is the 835th data value, which is 2.
(d) The mean is larger than 2 because the data is skew right by a few high values.
3.12.
Eastern Europe
Leaves (1)
87
995554
7321100
Stem (10)
0
1
2
3
4
5
6
7
8
Middle East
Leaves (1)
4
9
9
489
029
1
Eastern Europe: mean ๏ฝ 77.7, standard deviation ๏ฝ 5.4, minimum ๏ฝ 67.0, Q1 ๏ฝ 75.0, median ๏ฝ 79.0,
Q3 ๏ฝ 81.0, maximum ๏ฝ 87.0
Middle East: mean ๏ฝ 37.5, standard deviation ๏ฝ 20.0, minimum ๏ฝ 4.0, Q1 ๏ฝ 29.0, median ๏ฝ 38.5, Q3 ๏ฝ 42.0,
maximum ๏ฝ 81.0
Female economic activity seems greater, on average, in Eastern Europe than in the Middle East. Except for
standard deviation, all of the descriptive statistics in Eastern Europe exceed the descriptive statistics in the
Middle East. There appear to be more women in the labor force (per 100 men) in Eastern Europe than in the
Middle East.
Copyright ยฉ 2018 Pearson Education, Inc.

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