Page 1
Full file at https://fratstock.eu
INSTRUCTOR’S MANUAL
to accompany
STATISTICAL METHODS FOR THE SOCIAL SCIENCES
Fourth Edition
Alan Agresti and Barbara Finlay
published by Pearson Education
Manual prepared by:
Jackie Miller 404 Cockins Hall
Department of Statistics
The Ohio State University
Columbus, OH 43210
Instructors: Please notify Alan Agresti of any errors in this manual or the text so they can be
corrected for future printings. Please send e-mail to [email protected] .
Page 2
Full file at https://fratstock.eu
Table of Contents
1. Introduction 1
2. Sampling and Measurement 2
3. Descriptive Statistics 5
4. Probability Distributions 20
5. Statistical Inference: Estimation 29
6. Statistical Inference: Significance Tests 39
7. Comparison of Two Groups 50
8. Analyzing Association Between Categorical Variables 64
9. Linear Regression and Correlation 71
10. Introduction to Multivariate Relationships 90
11. Multiple Regression and Correlation 95
12. Comparing Groups: Analysis of Variance (ANOVA) Methods 109
13. Combining Regression and ANOVA: Quantitative and Categorical Predictors 116
14. Model Building with Multiple Regression 123
15. Logistic Regression: Modeling Categorical Responses 139
16. An Introduction to Advanced Methodology 145
Page 3
Full file at https://fratstock.eu
1
Chapter 1
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 million voters. (b) A statistic is the 56.5% who voted for Schwarzenegger from the
exit poll sample of size 2705; a parameter is the 55.9% who actually voted for Schwarzenegger.
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. A statistic, since it is based on the approximately 1200 Floridians 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 ―yes, definitely‖ or ―yes, probably.‖ (b) In 1998, a total of 85.8%
said ―yes, definitely‖ or ―yes, probably.‖ (c) A total of 74.4% said ―yes, definitely‖ or ―yes,
probably.‖ 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. (a)
1.10.
Race Age Sentence Felony? Prior
Arrests
Prior
Convictions
white 19 2 no 2 1
black 23 1 no 0 0
white 38 10 yes 8 3
Hispanic 20 2 no 1 1
white 41 5 yes 5 4
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,
Page 4
Full file at https://fratstock.eu
2
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.
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. (b) The population of interest is
women in New England in the early eighteenth century.
1.17. (a) A statistic is the 45% of the sample of subjects interviewed in the UK who said yes. (b)
A parameter is the true percent of the 48 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 10% (in
Bulgaria) to 60% in Luxembourg). (d) An inferential analysis is that the percentage of adults in
the UK who would say yes falls between 41% and 49%.
Chapter 2
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) Nominal (b) Nominal (c) Interval (d) Nominal (e) Nominal (f) Ordinal (g) Interval (h)
Ordinal (i) Nominal (j) Interval (k) Nominal
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.
Page 5
Full file at https://fratstock.eu
3
2.7. (a) Ordinal, since there is a sense of order to the categories. (b) Discrete. (c) These values are
statistics since them come from a sample.
2.8. Ordinal.
2.9. (b), (c), (d)
2.10. (a), (c), (e), (f)
2.11. Students numbered 10, 22, 24.
2.12. Number names 00001 to 52000. First five that are selected are 15011, 46573, 48360, 39975,
06907.
2.13. 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 –2.4% for Gore, 0.1% for Bush, and 1.3% for Nader.
2.16. (a) This is a volunteer sample because viewers chose whether to call in. (b) Randomly
sample the population.
2.17. The first question is confusing in its wording. The second question has clearer wording.
2.18. (a) Skip number is k = 52,000/5 = 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 + 10400 = 11936, 11936 + 10400 = 22336, 22336 +
10400 = 32736, 32736 + 10400 = 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 ―Martinez‖ 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 = 5000/100 = 50.
2.20. (a) This is not a simple random sample since the sample with necessarily have 40 women
and 40 men. A simple random sample may or may not have exactly 40 men and 40 women. (b)
This is stratified random sampling. You ensure that neither men nor women are over-sampled.
Page 6
Full file at https://fratstock.eu
4
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 represented—the 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.
2.24. (a) Draw a systematic sample from the student directory, using skip number k = N/100,
where N = 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, 2-4
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.
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.
Page 7
Full file at https://fratstock.eu
5
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.
2.33. 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. (b)
2.35. (c)
2.36. (c)
2.37. (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.
Chapter 3
3.1. (a)
Place of Birth Relative Frequency
Europe 13.7%
Asia 25.4%
Caribbean 9.6%
Central America 37.6%
South America 6.1%
Other 7.6%
Page 8
Full file at https://fratstock.eu
6
(b)
Place of Birth
S AmericaOtherCaribbeanEuropeAsiaC America
Perc
en
t
40.00
30.00
20.00
10.00
0.00
(c) ―Place of birth‖ is categorical. (d) The mode is Central America.
3.2. (a)
Religion Relative Frequency
Christianity 41.2%
Islam 25.5%
Hinduism 17.6%
Confucianism 7.8%
Buddhism 7.8%
Page 9
Full file at https://fratstock.eu
7
(b)
Religion
ConfucianismBuddhismHinduismIslamChristianity
Rela
tiv
e F
req
uen
cy
50.00
40.00
30.00
20.00
10.00
0.00
(c) The mode of these five 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)
Midterm_Score
10090807060
Fre
qu
en
cy
12.5
10.0
7.5
5.0
2.5
0.0
Histogram
Mean =82.88Std. Dev. =8.947
N =33
Page 10
Full file at https://fratstock.eu
8
3.4. (a)
Number Persons Relative Frequency
1 27.1%
2 33.3%
3 16.0%
4 13.8%
5 or more 9.8%
(b)
Number of Persons
5 or more4321
Rela
tiv
e F
req
uen
cy
40.00
30.00
20.00
10.00
0.00
(c) The median household size is 2 persons, and the mode is also 2 persons.
3.5. (a)
Frequency Percent Cumulative
Percent
Valid 1 3 6.0 6.0
2 8 16.0 22.0
3 9 18.0 40.0
4 2 4.0 44.0
5 8 16.0 60.0
6 9 18.0 78.0
7 5 10.0 88.0
8 2 4.0 92.0
9 2 4.0 96.0
10 1 2.0 98.0
13 1 2.0 100.0
Total 50 100.0
Page 11
Full file at https://fratstock.eu
9
(b)
MU_noDC
12.5107.552.50
Fre
qu
en
cy
10
8
6
4
2
0
Histogram
Mean =4.8Std. Dev. =2.571
N =50
The distribution appears to be bimodal and skewed to the right.
(c) Stem Leaves
1 000
2 00000000
3 000000000
4 00
5 00000000
6 000000000
7 00000
8 00
9 00
10 0
11
12
13 0
The stem-and-leaf plot shows the same bimodality and right skew that the histogram does.
3.6. (a) GDP is rounded to the nearest thousand Stem (10 thousands) Leaves (thousands
2 023
2 58899
3 00011122233
3 8
4
4
5
5
6
6
7 0
Page 12
Full file at https://fratstock.eu
10
(b)
RoundGDP
70.0060.0050.0040.0030.0020.00
Fre
qu
en
cy
12.5
10.0
7.5
5.0
2.5
0.0
Histogram
Mean =32.00Std. Dev. =9.615
N =23
(c) The outlier in each plot is Luxembourg.
3.7. (a) The mean is (26 + 17 + 236 + 2 + 6)/5 = 287/5 = 57.4 abortions per 1000 women 15 to 41
years of age. (b) The median is 17 abortions per 1000 women 15 to 41 years of age. The mean
and median are so different because California is an extreme outlier in this small data set.
3.8. (a) The mean is (0.3 + 1.8 + 2.3 + 1.2 + 1.4 + 0.7 + 9.9 + 20.1)/8 = 37.7/8 = 4.7 metric tons
per person. The median is 1.6 metric tons per person. (b) The United States appears to be an
outlier, since it is far greater than any other data value. (Without the United States, the mean is
2.5 and the median is 1.4.)
3.9. (a) The response ―not far enough‖ is the mode. (b) We cannot compute and mean or median
with these data since they are categorical.
3.10. (a) Stem Leaves
0 4679
1 133
2 0
3 9
4 4
(b) The mean is 16.6 days, and the median is 12 days.
(c) Leaves
25 years ago Stem Leaves
0 4679
875 1 133
440 2 0
21 3 9
0 4 4
5 5
For the data from 25 years ago, the mean was 27.6 days, and the median was 24 days. The mean
has decreased by 11 days, and the median has decreased by 12 days since 25 years ago. (d) Of the
Page 13
Full file at https://fratstock.eu
11
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 Frequency Relative Frequency
0 79 4.0
1 422 21.2
2 577 29.0
3 337 17.0
4 226 11.4
5 136 6.8
6 99 5.0
7 23 1.2
8 34 1.7
9 4 0.2
10 23 1.2
12 14 0.7
13 1 0.1
14 7 0.4
15 2 0.1
18 2 0.1
24 1 0.1
Total 1987 100.0
(b) The distribution is unimodal and right skewed. (c) The median is the 994th 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. Central
America Stem
Western
Europe
8540 4
85210 5 488
82 6 003678
7 1268
8 567
9 0
Female economic activity seems greater, on average, in Western Europe than in Central America.
Most of the values in Western Europe exceed the highest value in Central America. There appear
to be more women in the labor force (per 100 men) in Western Europe than in Central America.
3.13. Since the mean is much greater than the median, the distribution of 2000 household income
in Canada is most likely skewed to the right.
3.14. (a) The median is ―2 or 3 times a month.‖ The mode is ―not at all.‖ The data are centered
around the respondents having sex about 2 or 3 months in the past 12 months. The most frequent
answer to the question is ―not at all.‖ (b) The sample mean is 4.1, which means that, on average,
the respondents had sex about 4 times a month in the past 12 months.
3.15. (a) The mode is ―every day.‖ The median is ―a few times a week.‖ (b) The mean is 3.7
times per week, which is lower than the 4.4 times a week in 1994.
Page 14
Full file at https://fratstock.eu
12
3.16. (a) For each gender, the distribution of earnings is skewed to the right, since each mean is
greater than its respective median. (b) The overall mean income is ($39,890×73.8 +
$56,724×83.4)/(73.8 + 83.4) = $7674663.6/157.2 = $48,821.
3.17. (a) The response variable is median family income, and the explanatory variable is race. (b)
We cannot find the median income for the combined groups since we do not know how many
families are in each group. (c) We would need to know how many families were in each group.
3.18. (a) The distribution is skewed to the right. (b) The Empirical Rule only applies to bell-
shaped distributions, so it does not apply here. (c) The median is 0. If the 500 observations were
to shift from 0 to 6, the median would remain zero, since half of the data values fall below 0 and
half fall above 0. This illustrates the resistance of the median to skewness and extreme values.
3.19. (a) Median: $10.13; mean: $10.18; range: $0.46; standard deviation: $0.22. (b) Median:
$10.01; mean: $9.17; range: $5.31; standard deviation: $2.26. The median is resistant to outliers,
but the mean, range, and standard deviation are highly impacted by outliers.
3.20. (a) Mean: 30; standard deviation: 9.0. (b) Minimum: 13; lower quartile: 25.5; median: 31;
upper quartile: 36; maximum: 42.
3.21. The mean is 28.7, and the standard deviation is 12.5. The 2006 HDI ratings for the top 10
nations vary greatly.
3.22. (a) The life expectancies in Africa vary more than the life expectancies in Western Europe,
because the life expectancies for the African countries are more spread out than those for the
Western European countries. (b) The standard deviation is 1.1 for the Western European nations
and 7.1 for the African nations.
3.23. (a) (i) $40,000 to $60,000; (ii) $30,000 to $70,000; (iii) $20,000 to $80,000. (b) A salary of
$100,000 would be unusual because it is 5 standard deviations above the mean.
3.24. (a) Approximately 68% of the values are contained in the interval 32 to 38 days;
approximately 95% of the values are contained in the interval 29 to 41 days; all or nearly all of
the values are contained in the interval 26 to 44 days. (b) (i) The mean would decrease if the
observation for the U.S. was included. (ii) The standard deviation would increase if the
observation for the U.S. was included. (c) The U.S. observation is 5.3 standard deviations below
the mean.
3.25. (a) 88.8% of the observations fall within one standard deviation of the mean. (b) The
Empirical Rule is not appropriate for this variable, since the data are highly skewed to the right.
3.26. 10 is realistic; –20 is impossible since the standard deviation cannot be negative; 0 implies
that every student scored 76 on the exam, which is highly improbable; 50 is too large (it is half of
the possible range of scores).
3.27. (a) The most realistic value is 0.4, because the range is 5 times the length of this value. (b)
The value of –10.0 is impossible since the standard deviation cannot be negative.
3.28. (d)
Page 15
Full file at https://fratstock.eu
13
3.29. (a) Since the range is 43.5 standard deviations above the mean, the distribution is most
likely skewed to the right. (b) The distribution probably has outliers (take the maximum usage,
for example).
3.30. The distribution is most likely skewed to the right since the minimum water consumption (0
thousands of gallons) is less than one standard deviation below the mean.
3.31. (a) The range is $28,700, which is the difference between the mean salary for secondary
school teachers in Illinois (highest mean) and in South Dakota (lowest mean). (b) The
interquartile range is $9600 and represents the spread of the mean salaries for the middle 50% of
the states.
3.32. (a)
40000
50000
60000
Sala
ry
(b) The box plot suggests that the data are skewed to the right. (c) 7000 is the most plausible
standard deviation, since the range of the data is about 4 standard deviations. The values 100 and
1000 are too small for the spread that we see, and 25,000 is just slightly over the value for the
range.
3.33. The mean, standard deviation, maximum, and range all decrease, because the observation
for D.C. was a high outlier. Note that these statistics are not resistant to outliers. On the other
hand, the median, Q3, Q1, the interquartile range, and the mode remain the same, as these are all
resistant to outliers. The minimum remains the same since D.C. was a high outlier and not a low
outlier.
3.34. (a) The Empirical Rule does not apply to this distribution because the standard deviation is
much larger than the mean, suggesting a right-skewed distribution. (b) The five-number summary
confirms that the distribution is skewed to the right, since the distance between Q3 and the
medians is larger than the distance between the median and Q1 and the maximum is so large. (c)
IQR = Q3 – Q1 = 1105 – 256 = 849. Low outliers would be observations less than Q1 – 1.5(IQR)
= 256 – 1.5(849) = –1017.5. There are no values that are low outliers. High outliers would be
observations greater than Q3 + 1.5(IQR) = 1105 + 1.5(849) = 2378.5. At least the maximum is a
high outlier.
Page 16
Full file at https://fratstock.eu
14
3.35. (a) The sketch should show a right-skewed distribution. (b) The sketch should show a right-
skewed distribution. (c) The sketch should show a left-skewed distribution. (d) The sketch should
show a right-skewed distribution. (e) The sketch should show a left-skewed distribution.
3.36. (a) Skewed to the left (b) Bell shaped (c) Skewed to the right (d) Skewed to the left (e)
Skewed to the left (f) Skewed to the right (g) U shaped
3.38. A box plot using only the five-number summary follows:
4.0
6.0
8.0
10.0
12.0
EU
un
em
plo
ym
en
t
This box plot shows us that the maximum is an outlier. Since the mean and the median are the
same, the distribution may be slightly more symmetric than the box plot implies. It is important to
note that only the five-number summary was used to produce this box plot.
3.39. (a) Minimum = 0, Q1 = 20, median = 30, Q3 = 50, maximum = 14. (b) Same as part (a). (c)
The observations with values 12 and 14 are outliers. (d) The standard deviation is 3. The value
0.3 is too small for the distribution, the value 13 is almost equal to the range, and the value 23
exceeds the range.
3.40. Side-by-side box plots are not very informative as shown below:
Page 17
Full file at https://fratstock.eu
15
The infant mortality rates in Africa are much higher than the infant mortality rates in Western
Europe. In addition, since Q1, the median, and Q3 are all equal for Western Europe, we do not
actually see a ―box‖ in the box plot. Infant mortality rates in Africa are skewed to the right, while
infant mortality rates in Western Europe are symmetric.
3.41. (a)
10.0
15.0
20.0
25.0
No
he
alt
h i
nsu
ran
ce
(b) The distribution appears to be skewed to the right.
3.42. (a) The range is 92.3 – 78.3 = 14. The interquartile range is 88.8 – 83.6 = 5.2. (b) Low
outliers would be observations less than Q1 – 1.5(IQR) = 83.6 – 1.5(5.2) = 75.8. There are no
values that are low outliers. High outliers would be observations greater than Q3 + 1.5(IQR) =
88.8 + 1.5(5.2) = 96.6. There are no values that are high outliers.
3.43. (a) Minimum = 1, Q1 = 3, median = 5, Q3 = 6, maximum = 13. (b)
2.5
5.0
7.5
10.0
12.5
MU
_n
oD
C
Louisiana appears to be a mild outlier. (c) Minimum = 1, Q1 = 3, median = 5, Q3 = 6, maximum
= 44.
Page 18
Full file at https://fratstock.eu
16
0
10
20
30
40M
U
Louisiana is still a mild outlier, and D.C. is an extreme outlier. Only the maximum changes in the
five-number summary when the observation for D.C. is added to the data set.
3.44. The IQR is most likely 350. The value of 1500 is the range. The value of –10 is impossible
for an IQR, and the 0 would only occur if all data values were the same. Given the minimum,
median, and maximum, the value 10 is too small to be the IQR.
3.45. (a) Luxembourg’s observation is 3.9 standard deviations above the mean. (b) Sweden’s
observation is 0.8 standard deviations below the mean. (c) (i) Canada’s observation is 2.5
standard deviations above the mean of the EU countries. (ii) The U.S. observation is 3.6 standard
deviations above the mean of the EU countries (but not as high as Luxembourg).
3.46. (a) Italy’s observation is 0.4 standard deviations below the mean. (b) The U.S. observation
is 3.4 standard deviations above the mean of the EU countries. (c) We expect almost all of the
values in a bell shaped distribution to be within 3 standard deviations of the mean. Thus, the U.S.
observation would be considered a high outlier.
3.47. (a) Response variable: opinion about national health insurance (favor, oppose); explanatory
variable: political party (Democrat, Republican). (b) The data could be summarized in a
contingency table with political party as the rows and opinion about national health insurance as
the columns.
3.48. (a) Response variable: happiness; explanatory variable: religious attendance. (b) For those
who attend religious services nearly every week or more, 44.5% reported being very happy. For
those who attend religious services never or less than once a year, 23.2% reported being very
happy. (c) There appears to be an association between happiness and religious attendance since
the percentages that reported being very happy differed greatly by attendance at religious
services.
3.49. (a) United States: predicted fertility = 3.2 – 0.04(50) = 1.2; Yemen: predicted fertility = 3.2
– 0.04(0) = 3.2. (b) The negative value implies that the fertility rate decreases as Internet use
increases.
Page 19
Full file at https://fratstock.eu
17
3.50. (a) Points in a scatterplot for these data should have a negative association and be fairly
tightly clustered in a linear pattern. (b) Contraceptive use is more strongly associated with fertility
than is Internet use because –0.89 is a stronger linear association than is –0.55.
3.51. (a) Based on the plot (see next page), the correlation should be positive, since higher values
of GDP tend to go with higher values of CO2 (and vice versa). (b) Luxembourg has a GDP of
69,961 and CO2 of 22.0, both of which are extreme values.
GDP
70,00060,00050,00040,00030,00020,00010,000
CO
2
25.0
20.0
15.0
10.0
5.0
3.52. The number of physicians is more strongly correlated with carbon dioxide emissions than is
female economic activity, since the absolute value of the correlation for number of physicians and
CO2 emissions is closer to 1 than is the correlation for female economic activity and CO2
emissions.
3.53. (a) y is a sample statistic (sample mean) used to estimate the population mean µ. (b) s is a
sample statistic (sample standard deviation) used to estimate the population standard deviation .
3.54. (a) The mean is 1232.2 miles, with standard deviation 1681.7 miles. The median is 640
miles. The minimum distance from home is 0 miles, while the maximum distance is 8000 miles.
The histogram shows that the distribution of the distance from home is skewed to the right.
Page 20
Full file at https://fratstock.eu
18
DHome
80006000400020000
Fre
qu
en
cy
40
30
20
10
0
Histogram
Mean =1232.2Std. Dev. =1681.748
N =60
(b) The mean is 7.3 hours, with standard deviation 6.7 hours. The median is 6 hours. The
minimum from home is 0 hours, while the maximum is 37 hours. The histogram shows that the
distribution of the hours of watching television is skewed to the right.
TVhours
40.030.020.010.00.0
Fre
qu
en
cy
20
15
10
5
0
Histogram
Mean =7.27Std. Dev. =6.717
N =60
3.56. Report should include graphical displays and summary statistics. The summary statistics
are: mean = 2.7, standard deviation = 2.1, minimum = 0.1, Q1 = 1.5, median = 2.1, Q3 = 3.6,
maximum = 9.4. The U.S. is an outlier with 9.4 gun deaths per 100,000 people.
3.57. Report should state that the explanatory variable is the percentage with income below the
poverty level and the response variable is the violent crime rate. The correlation coefficient is
0.496. D.C. appears to be an outlier.
