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Statistical Methods For The Social Sciences 5th Global Edition Alan Agresti - Solutions

9. The news media report that a study has found that children who eat breakfast get better math grades than those who do not eat breakfast This result was based on a simple bi- variate association. with X=whether cat breakfast (yes, no) and Y = grade in last math course taken. How might this result
10. For a particular Big Ten university, the mean income for male faculty is $8000 higher than the mean income for female faculty. Explain how this difference could disappear.a) Controlling for number of years since received highest degree. if male professors tend to be older and inore expenenced,
11. Refer to the variables in Table 9.4. The number of bedrooms has a moderately strong positive correlation with selling price (r 59). Contolling for size of home, however, this association diminishes greaily Explain how this could happen, illustrating with a diagram showing potential direct and
12. Refer to the variables in Table 9.16 Perhaps surprisingly, a moderate positive correla- tion exists between crime rate and percent who are at least high school graduates (r = .468). Percentage living in metropolitan areas is also strongly positively correlated both with come rate (r = .678) and
13 Give an example of three vanables for which the effect of X, on y would bea) Spurious, disappearing when X2 is controlled.b) Part of a chain relationship, disappearing when an intervening variable X2 is controlled.c) Weakened, but not eliminated, when X, is controlledd) Unaffected by controlling
14. Opposition to the legal availability of abortion is stronger among the very religious than the nonreligious, and it is also stronger among those with conservative sexual attitudes than those with more permissive attitudes.a) Draw a inec-variable diagram of how these variables might be related,
15. Table 10 10 lists the mean salary, in thousands of dollars, of full-time instructional faculty on nine-month contracts in United States institutions of higher education in 1993-1994, by gender and i ank.a) Suppose that gender is the explanatory variable. Identify the response variable and the
16 Refer to Table 10.11 Form the overall table. summing over social class Compare the proportions of Catholics and Protestanis favoring the death penalty, both ignoring and controlling social class. What type of relationship do these data satisfy? TABLE 10.11 Social Class Working Class Middle Class
17. Refer to Table 15.4 on death penalty verdict, defendant's race, and victims' race.a) Construct the bivanate table relating defendant's race to death penalty verdict. ignor- ing victims race Calculate the conditional distribution on the death penalty verdict. for each race of defendant.b)
18. For the cell counts in Table 10.12 iclating Y = exam score (I = below median. 2 = above median) to gender, controlling for subject of exam (Math. Verbal).a) Is subject of exam a suppressor variable? Explain.b) Is there interaction? Explain. TABLE 10.12 Math Verhal Gender y=1 Y = 2 Y = 1 Y = 2
19. Refer to Problem 8.42 in Chapter 8.a) Treat expectation of voting as the control variable, and construct the partial tables re- lating political party affiliation to present voting intentionb) Show how to combine the partial tables to obtain the bivariate table constructed in Problem 8.43.c)
20. Refer to Table 15.17 on AZT use and AIDS symptoms.a) Using the difference of proportions or the odds ratio. describe the association for (i) whites. (ii) blacks.b) Does there seem to be strong evidence of statistical interaction? Explain.
21. A study of the association between whether a smoker (yes. nor and whether have had some form of cancer (yes, no) has odds ratio 1 1 for subjects of age less than 30. 2.4 for subjects of age 30 to 50, and 4.3 for subjects of age over 50.a) Identify the response variable, explanatory variable.
22. Refer to Table 8.29 Treat the four groups as a cross-classification of the two variables, race and gender. Treating race as a control variable, is there evidence of severe statistical interaction for these data? Explain.
23. A study of students at Oregon State University found an association between frequency of church attendance and favorability toward the legalization of marijuana. Both variables were measured in ordered categories When gender of student was controlled, the result- ing gamma measures for the two
24. 4 study of the relationship between student's high school GPA and mother's employment (yes, no) suspects an interaction with gender of student. Controlling gender of student, Table 10.13 contains the mean GPA for each combination of gender and mother's em- ployment.a) Describe the relationship
25. Refer to the WWW data set (Problem 17). Construct partial tables relating opinion about abortion to opinion about life after death, controlling for attendance at religious services, ineasured using the two categories, (Never or occasionally. Most weeks or every week). Prepare a report (a)
26 Refer to Problem 1.7. Repeat the previous problem for three variables chosen by your instructor
27. Refer to Problem 1.7. Are there any pairs of these variables for which you expect the association to disappear under control for a third variable? Explain.
28. Using the most recent General Social Survey, construct a contingency table relating gen- der and party affiliation ("PARTYID"). Is there still a gender gap? Control for political ideology ("POLVIEWS") by forming partial tables for the most conservative and the most liberal subjects. Does the
29. Table 10.14 is a contingency table that shows counts on self-esteem, race, and cumulative GPA, for a sample of females. Analyze the type of multivariate relationship that these variables seem to satisfy. Prepare a report, explaining the analyses you conducted to reach your conclusion and
30. Table 10.15 shows the relation between attitude toward a nuclear freeze and church atten- dance, controlling for educational levels of the respondents. Assessing association by the difference of proportions, analyze these data using methods of this chapter, and explain why it is misleading to
31. In 1980. SAT total scores (verbal plus math) had a mean of 890. In 1984 the mean in- creased to 897. for an increase of 7. Table 10.16 shows the means and their changes, con- trolling for race. For each year, the table also shows the percentage representation in the sample of each race.a) In
32 Table 10.17 reports the median family income (in dollars) in 1992 for white and black families The median for white families is $17.748 higher than the median for black fam- ilies. For each of the three types of families, however, the median for white families is about $8000 higher than the
33. Table 10.18 shows the mean number of children in Canadian families, classified by whether the family was English speaking or French speaking and by whether the family was in Quebec or in another province. Let = number of children in family. X = primary language of family, and X = province
34 Religious affiliation is associated with attitudes about racial intermaniage, with white Catholics tending to be less racially prejudiced than Protestants, members of theologically liberal Protestant groups tending to be less prejudiced than those from the more conser- vative denominations, and
35. A research study funded by Wobegon Springs Mineral Water, Inc., discovers that the prob- ability that a newborn child has a birth defect is lower for families that regularly buy bot- tled water than for families that do not. Is this association likely to reflect a causal link between drinking
36 The percentage of women who get breast cancer is higher now than at the beginning of this century. Suppose that cancer incidence tends to increase with age, and suppose diar women tend to live longer lives now than earlier in this century. Explain why a compar ison of breast cancer rates now
37. Refer to Table 91. A regression analysis reveals a moderately strong negative correla- tion (-.677) between percent of white residents and violent crime rate. Another vanable incasured in Table 91 is percent of families headed by a single parent. This is positively correlated with violent crime
38. In the United States median age of residents is lowest in Utah At each age level. the death rate from heart disease is higher in Utah than in Colorado; yet overall. the death rate from heart disease is lower in Utah than Colorado. Are there any contradictions here, or is this possible? Explain.
39 For lower-level managerial employees of a fast-food chain. the prediction equation relat- ing Y = amual income (thousands of dollars) to X = number of years experience on the= job equals 14.2+ 1.1X, for X = males and 14.2+.4X, for X = females. These equations show evidence of (select one, and
40 Statistical interaction refers to which of the following?a) Association exists between two vanablesb) The degree of association between two variables varies gicatly over the partial levels of a control vanable.c) The partial association is the same at each level of the control variable, but it
41. Consider the relationship between political party preference (Democrat. Republican) and X, ace (Black, White) and X2 = gender. There is an association between Y and both X1 and X2, with the Democrat preference being more likely for blacks than whites and for women than men Select the coniect
To construct a confidence interval for a proportionπ, it is not necessary to substitute πˆ for the unknown value of π in the formula for the true standard error of πˆ . A less approximate method (called the score confidence interval for a proportion) finds the endpoints for a 95% interval by
8.45.* For a 2×2 table with cell countsa, b,c, d, the sample log odds ratio logˆθ has approximately a normal sampling distribution with estimated standard errorThe antilogs of the endpoints of the confidence interval for log(θ) are endpoints of the confidence interval for θ.For Table 8.14 on
Figure 9.20 is a scatterplot relating y =percentage of people using cell phones and x = per capita gross domestic product (GDP) for some nations listed in the Human Development Report.(a) Give the approximate x- and y-coordinates for the nation that has the highest (i) cell phone use, (ii) GDP.(b)
For the Houses data file (shown partly in Table 9.5), Table 9.12 shows a regression analysis relating selling price to number of bedrooms.(a) Report the prediction equation, and interpret the slope.(b) Report r2, and interpret its value.(c) Report the correlation and its confidence interval, and
Is political ideology associated with income? When GSS data for 1478 cases in 2014 were used to regress y =political views (POLVIEWS, using scores 1–7 with 1 = extremely liberal and 7 = extremely conservative) on x =respondent’s income (RINCOME, using scores 1–12 for the 12 income
Refer to Table 9.1 (page 260), available in the Crime2 data file at the text website. Pose a research question about the relationship between the murder rate and the percentage of single-parent families. Using software, conduct analyses to address this question. Write a report showing your analyses
9.65.*Refer to the previous exercise. Let ρ1 and ρ2 denote the population correlation values between two variables for two separate populations. Let r1 and r2 denote sample values for independent random samples from the populations.To test H0: ρ1 = ρ2, the test statistic iswhere T1 and T2 are
9.67.* The formula for the correlation can be expressed as(a) Using the first formula, explain why the correlation has the same value when x predicts y as when y predicts x.(b) By the second formula, the correlation is approximately the average product of the z-score for x times the z-score for y.
9.69.* Suppose that the linear regression model E(y) = α + βx with normality and constant standard deviation σ is truly appropriate. Then, the interval of numberspredicts where a new observation on y will fall at that value of x. This interval, which for large n is roughly ˆy ± 2s, is a 95%
Table 10.6 relates occupational level (white collar, blue collar) and political party choice, controlling for income.(a) Construct the bivariate table between occupational level and political party, ignoring income. Is there an association? If so, describe it.(b) Do the partial tables display an
In murder trials7 in 20 Florida counties in two years, the death penalty was given in 19 out of 151 cases in which a white killed a white, in 0 out of 9 cases in which a white killed a black, in 11 out of 63 cases in which a black killed a white, and in 6 out of 103 cases in which a black killed a
A regression analysis with recent UN data from several nations on y = percentage of people who use the Internet, x1 = per capita gross domestic product (in thousands of dollars), and x2 = percentage of people using cell phones has results shown in Table 11.12.(a) Write the prediction equation.(b)
Refer to the previous exercise. Using software with the Florida data file at the text website,(a) Construct box plots for each variable and scatterplots and partial regression plots between y and each of x1 and x2. Interpret these plots.(b) Find the prediction equations for the (i) bivariate
Refer to the previous exercise.(a) Report the F statistic for testing H0: β1 = β2 = 0, report its df values and P-value, and interpret.(b) Show how to construct the t statistic for testing H0:β1 = 0, report its df and P-value for Ha: β1 = 0, and interpret.(c) When we add x3 = percentage of
Exercise 11.11 showed a regression analysis for statewide data on y = violent crime rate, x1 = poverty rate, and x2 = percentage living in urban areas. When we add an interaction term, we get ˆy = 158.9 − 14.72x1 −1.29x2 + 0.76x1x2.(a) As the percentage living in urban areas increases, does
Table 11.19 shows results of regressing y = birth rate (number of births per 1000 population) on x1 =women’s economic activity and x2 = literacy rate, using UN data for 23 nations.(a) Report the value of each of the following:(i) ryx1, (ii) ryx2, (iii) R2,(iv) TSS, (v) SSE, (vi) mean square
Amultiple regression model describes the relationship among a collection of cities between y = murder rate(number of murders per 100,000 residents) and x1 =number of police officers (per 100,000 residents), x2 = median length of prison sentence given to convicted murderers(in years), x3 = median
For the 2014 GSS, Table 11.20 shows estimates(with se values in parentheses) for four regression models for y = political party identification in the United States, scored from 1 = strong Democrat to 7 = strong Republican. The explanatory variables are number of years of education in model 1, also
Refer to Examples 11.1 (page 320) and 11.8(page 343). Explain why the partial correlation between crime rate and high school graduation rate is so different(including its sign) from the bivariate correlation.
Refer to the previous exercise.(a) Find the partial correlation between y and x1, controlling for x2. Interpret the partial correlation and its square.(b) Find the estimate of the conditional standard deviation, and interpret.(c) Show how to find the estimated standardized regression coefficient
A recent study5 analyzed the effect of x1 = work hours per day and x2 = commuting time to work on y = political participation. For the cluster sample of 1001 adult Americans, ¯x1 = 8.4 hours (s = 2.4) and ¯x2 = 19.8 minutes (s = 13.6). Political participation, which was a composite variable based
A multiple regression analysis investigates the relationship between y = college GPA and several explanatory variables, using a random sample of 195 students at Slippery Rock University. First, high school GPA and total SAT score are entered into the model. The sum of squared errors is SSE = 20.
Use software with the Houses data file to allow interaction between number of bedrooms and number of bathrooms in their effects on selling price.(a) Interpret the fit by showing the prediction equation relatingˆy and number of bedrooms for homes with (i) two bathrooms, (ii) three bathrooms.(b)
A study analyzes relationships among y = percentage vote for Democratic candidate, x1 = percentage of registered voters who are Democrats, and x2 = percentage of registered voters who vote in the election, for several congressional elections in 2016. The researchers expect interaction, since they
Refer to the previous exercise.(a) Test the partial effect of number of bathrooms, and interpret.(b) Find the partial correlation between selling price and number of bathrooms, controlling for number of bedrooms.Compare it to the correlation, and interpret.(c) Find the estimated standardized
Refer to the Students data file. Using software, conduct a regression analysis using either (a) y = political ideology with explanatory variables number of times per week of newspaper reading and religiosity, or (b) y =college GPA with explanatory variables high school GPA and number of weekly
Use software with the Houses data file at the text website to conduct a multiple regression analysis of y =selling price of home (dollars), x1 = size of home (square feet), x2 = number of bedrooms, x3 = number of bathrooms.(a) Use scatterplots to display the effects of the explanatory variables on
Refer to the previous exercise. Find a 95% confidence interval for the change in the mean of y for a(a) 1-unit increase, (b) 50-unit increase in the percentage of adults owning homes, controlling for the other variables.Interpret.
For a random sample of 66 state precincts, data are available on y = percentage of adult residents who are registered to vote, x1 =percentage of adult residents owning homes, x2 = percentage of adult residents who are nonwhite, x3 = median family income (thousands of dollars), x4 =median age of
Refer to Table 11.5 on page 328. Test H0: β2 = 0 that mental impairment is independent of SES, controlling for life events.Report the test statistic, and report and interpret the P-value for (a) Ha: β2 = 0, (b) Ha: β2 < 0.
The General Social Survey has asked subjects to rate various groups using the “feeling thermometer.” The rating is between 0 and 100, more favorable as the score gets closer to 100 and less favorable as the score gets closer to 0. For a small data set from the GSS, Table 11.17 shows results of
Refer to the student data file created in Exercise 1.12.For variables chosen by your instructor, fit a multiple regression model and conduct descriptive and inferential statistical analyses. Interpret and summarize your findings.
Table 11.16 comes from a regression analysis4 of y = number of children in family, x1 = mother’s educational level in years (MEDUC), and x2 = father’s socioeconomic status (FSES), for a random sample of 49 college students at Texas A&M University.(a) Write the prediction equation. Interpret
For 2014 GSS data on y = highest year of school completed, x1 = mother’s highest year of school completed, and x2 =father’s highest year of school completed, we obtain ˆy = 9.86 + 0.345x1 (r2 = 0.195), ˆy = 10.15 +0.330x2 (r2 = 0.204), and ˆy = 9.30 + 0.194x1 + 0.212x2(R2 = 0.243). In a
Table 11.14 shows Stata output from fitting the multiple regression model to recent statewide data, excluding D.C., on y = violent crime rate (per 100,000 people), x1 = poverty rate (percentage with income below the poverty level), and x2 = percentage living in urban areas.(a) Report the prediction
Using industry-level data, a recent study6 analyzed labor’s share of income, measured as total compensation divided by total compensation plus the gross operating surplus. The authors predicted this would decrease as the degree of financialization of the company increased. Financialization was
For recentUNdata for several nations, a regression of carbon dioxide use (CO2, a measure of air pollution) on gross domestic product (GDP) has a correlation of 0.786.With life expectancy as a second explanatory variable, the multiple correlation is 0.787.(a) Explain how to interpret the multiple
Recent UN data from several nations on y = crude birth rate (number of births per 1000 population size), x1 = women’s economic activity (female labor force as percentage of male), and x2 = GNP (per capita, in thousands of dollars) has prediction equation ˆy = 34.53 −0.13x1 − 0.64x2. The
The Florida data file, shown partly on page 295, has data from the 67 Florida counties on y = crime rate(number per 1000 residents), x1 = median income (thousands of dollars), and x2 = percentage in urban environment.(a) Figure 11.12 shows a scatterplot relating y to x1. Predict the sign that the
Refer to the previous exercise.(a) Show how to obtain R-squared from the sums of squares in the ANOVA table. Interpret it.(b) r2 = 0.78 when GDP is the sole predictor. Why do you think R2 does not increase much when cell phone use is added to the model, even though it is itself highly associated
Use software with the Crime2 data file at the text website, with murder rate (number of murders per 100,000 people) as the response variable and with percentage of high school graduates and the poverty rate as explanatory variables.(a) Construct the partial regression plots. Interpret. Do you see
The Social Progress Index (see www.socialprogressimperative.org) is a measure of national progress in delivering social and environmental value.It is an average of three component measures: BHN =basic human needs, incorporating basic medical care and personal safety; FW = foundations of well-being,
For recent data in Jacksonville, Florida, on y = selling price of home (in dollars), x1 =size of home (in square feet), and x2 = lot size (in square feet), the prediction equation is ˆy = −10,536 + 53.8x1 + 2.84x2.(a) A particular home of 1240 square feet on a lot of 18,000 square feet sold for
For students at Walden University, the relationship between y = college GPA (with range 0–4.0) and x1 =high school GPA (range 0–4.0) and x2 = verbal college board score (range 200–800) satisfies E(y) = 0.20 +0.50x1 + 0.002x2.(a) Find the mean college GPA for students having (i)high school GPA
Consider the relationship between y = political party preference (Democrat, Republican) and x1 = race(Black, White) and x2 = gender. There is an association between y and both x1 and x2, with the Democrat preference being more likely for blacks than whites and for women than men.(a) x1 and x2 are
For the OECD data file at the text website, shown in Table 3.13 (page 70), pose a research question about how at least two of the variables shown in that table relate to carbon dioxide emissions. Conduct appropriate analyses to address that question, and prepare a one-page report summarizing your
Example 9.10 (page 280) used a data set on house sales to regress y = selling price of home (in dollars) to x= size of house (in square feet). The prediction equation was ˆy = −50,926 + 126.6x. Now, we regard size of house as x1 and also consider x2 = whether the house is new (yes or no). The
Statistical interaction refers to which of the following?(a) Association exists between two variables.(b) The effect of an explanatory variable on a response variable changes greatly over the levels of a control variable.(c) The partial association is the same at each level of the control variable,
For all court trials about homicides in Florida in a certain period, the difference between the proportions of whites and blacks receiving the death penalty was 0.026 when the victim was black and −0.077 when the victim was white.10 This shows evidence of (a) a spurious association,(b)
For recent U.S. presidential elections, in each state wealthier voters tend to be more likely to vote Republican, yet states that are wealthier in an aggregate sense are more likely to have more Democrat than Republican votes (Gelman and Hill 2007, Section 14.2). Sketch a plot that illustrates how
Using software with the Crime data file at the text website, conduct a regression analysis of violent crime rate with the explanatory variables poverty rate, the percentage living in urban areas, and the percentage of high school graduates. Prepare a report in which you state a research question
A study9 reported a correlation of 0.68 between scores on an index of depression and scores on an index that measures the amount of saturated fat intake. True or false:You can conclude that if you increase your saturated fat intake by a standard deviation, your degree of depression will increase by
Exercise 7.17 on page 219 mentioned a study of compulsive buying behavior that conducted a national telephone survey. The study found that lower-income subjects were more likely to be compulsive buyers. They reported,“Compulsive buyers did not differ significantly from other respondents in mean
Give an example of three variables for which the effect of x1 on y would be(a) Spurious, disappearing when x2 is controlled.(b) Part of a chain relationship, disappearing when a mediator variable x2 is controlled.(c) Weakened, but not eliminated, when x2 is controlled.(d) Unaffected by controlling
For the previous exercise, repeat the analysis, excluding the observation forD.C. Describe the effect of this observation on the various analyses.
A study of the relationship between student’s high school GPA and mother’s employment (yes, no) suspects an interaction with the gender of a student. Controlling gender, Table 10.10 shows results.(a) Describe the relationship between mother’s employment and GPA for females and for males. Does
For the UN data file at the text website (Table 3.9 on page 65), construct a multiple regression model containing two explanatory variables that provide good predictions for the fertility rate. How did you select this model?(Hint: One way uses the correlation matrix.)
The crude death rate is the number of deaths in a year, per size of the population, multiplied by 1000. According to the U.S. Bureau of the Census, recently Mexico had a crude death rate of 4.6 (i.e., 4.6 deaths per 1000 population) while the United States had a crude death rate of 8.4.Could the
The percentage of women who get breast cancer is higher now than a century ago. Suppose that cancer incidence tends to increase with age, and suppose that women tend to live longer now than a century ago. How might a comparison of breast cancer rates now with 100 years ago show different results
A research study funded by Wobegon Springs Mineral Water, Inc., discovers that the probability that a newborn child has a birth defect is lower for families that regularly buy bottled water than for families that do not.Does this association reflect a causal link between drinking bottled water and
In about 200 words, explain to someone who has never studied statistics what multiple regression does and how it can be useful.
A study observes that subjects who say they exercise regularly reported only half as many serious illnesses per year, on the average, as those who say they do not exercise regularly. The results section in the article states,“We next analyzed whether age was a confounding variable affecting this
Example 7.1 (page 194) discussed a study that found that prayer did not reduce the incidence of complications for coronary surgery patients.(a) Just as association does not imply causality, so does a lack of association not imply a lack of causality, because there may be an alternative explanation.
Analyze the Houses data file at the text website(and introduced in Example 9.10 on page 280), using selling price of home, size of home, number of bedrooms, and taxes. Prepare a one-page report summarizing your analyses and conclusions.
Eighth-grade math scores on the National Assessment of Educational Progress had means of 277 in Nebraska and 271 in New Jersey. For white students, the means were 281 in Nebraska and 283 in New Jersey. For black students, the means were 236 in Nebraska and 242 in New Jersey. For other nonwhite
Table 10.9 shows the mean number of children in Canadian families, classified by whether the family was English speaking or French speaking and by whether the family lived in Quebec or in another province. Let y =number of children in family, x1 = primary language of family, and x2 = province
Suppose that x1 = father’s education is positively associated with y = son’s income at age 40. However, for the regression analysis conducted separately at fixed levels of x2 = son’s education, the correlation does not differ significantly from zero. Do you think this is more likely to

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