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

8.42.* For2×2 tables, gamma simplifies to a measure first proposed about 1900 by the British statistician G. Udny Yule, who also introduced the odds ratio. In that special case, gamma is called Yule’s Q.(a) Show that for a generic table with counts (a,b) in row 1 and (c,d) in row 2, the number
If ˆy = 2 + 3x1 + 5x2 − 8x3,(a) ryx3 < 0.(b) ryx3·x1 < 0.(c) ryx3·x1,x2 < 0.(d) Insufficient information to answer.(e) Answers (a), (b), and (c) are all correct.
8.41.* Table 8.30 exhibits the maximum possible association between two binary variables for a sample of size n.(a) Show that X2 = n for this table and, hence, that the maximum value of X2 for 2 × 2 tables is n.(b) The phi-squared measure of association for 2×2 contingency tables has sample
Each subject in a sample of 100 men and 100 women is asked to indicate which of the following factors (one or more) are responsible for increases in crime committed by teenagers: A—the increasing gap in income between the rich and poor, B—the increase in the percentage of single-parent
The correct answer in Exercise 8.38(c) implies that if the chi-squared statistic is used for a contingency table having ordered categories in both directions, then (select the correct response(s))(a) The statistic actually treats the variables as nominal.(b) Information about the ordering is
Answer true or false for the following. Explain your answer.(a) Even when the sample conditional distributions in a contingency table are only slightly different, when the sample size is very large it is possible to have a large X2 test statistic and a very small P-value for testing H0:
The F test for comparing a complete model to a reduced model can be used to test(a) The significance of a single regression parameter in a multiple regression model.(b) H0: β1 = · · · = βp = 0 in a multiple regression equation.(c) H0: no interaction, in the model E(y) = α+β1x1 +β2x2 +β3x3
(a) When the sample size is very large, we have not necessarily established an important result when we show a statistically significant association. Explain.(b) The remarks in Sections 8.3 and 8.4 about small Pvalues not necessarily referring to an important effect apply for any significance test.
Shortly before a gubernatorial election, a poll asks a random sample of 50 potential voters the following questions:Party: Do you consider yourself to be a Democrat (D), a Republican (R), or an Independent (I)?Vote: If you were to vote today, would you vote for the Democratic candidate (D) or the
An abstract of an article6 dealing with alcohol use and sexual assault among college women stated,“This study prospectively examined the relation between alcohol use and sexual assault in a sample (n = 319) of first-year college women. ... Over the course of their freshman year, 19.3% reported
For 2014 GSS data, of those identifying as Democrats, 496 classified themselves as liberal and 171 as conservative. Of those identifying as Republicans, 56 called themselves liberal and 499 conservative. Using methods of this chapter, describe the strength of association, and interpret.TABLE 8.27
Does belief in evolution vary according to religious beliefs? Examine this using Table 8.28, for respondents to the 2014 General Social Survey. The variables are Fundamentalism/Liberalism of Respondent’s Religion and response to whether human beings developed from earlier species of animals.
Pose a research question about attitude regarding homosexual relations and political ideology. Using the most recent GSS data on variables HOMOSEX and POLVIEWS, conduct a descriptive and inferential analysis to address this question. Prepare a one-page report summarizing your analysis.
One year the GSS asked how housework was shared between the respondent and his or her spouse. Possible responses were 1 = I do much more than my fair share, 2 =I do a bit more than my fair share, 3 = I do roughly my fair share, 4 = I do a bit less than my fair share, 5 = I do much less than my fair
Refer to the data file you created in Exercise 1.12.For variables chosen by your instructor, pose a research question and conduct descriptive and inferential statistical analyses. Interpret and summarize your findings in a short report.
Explain the difference in the purposes of the correlation, the multiple correlation, and the partial correlation.
Refer to the Students data file (Exercise 1.11 on page 21). Using software, create and analyze descriptively and inferentially the contingency table relating opinion about abortion and (a) political affiliation, (b) religiosity.
Refer to Exercise 8.13 on happiness and income.The analysis there does not take into account the ordinality of the variables. Using software, summarize the strength of association by finding and interpreting gamma.Construct inference using it, and interpret.
A GSS cross-classified income in thousands of dollars(25) by job satisfaction (very dissatisfied, a little satisfied, moderately satisfied, very satisfied)for black Americans. Software provides the results shown in Table 8.26.TABLE 8.26| jobsat income | 1 2 3 4---------------------------------1 | 2
Let y = height, x1 = length of right leg, and x2 =length of left leg. Describe what you expect for the relative sizes of rx1x2, ryx2, R, and ryx2·x1.
For the 2014 GSS, γˆ = 0.19 for the relationship between job satisfaction (categories very dissatisfied, little dissatisfied, moderately satisfied, very satisfied) and family income (below average, average, above average).(a) Would you consider this a very strong or relatively weak association?
Table 8.25 cross-classifies happiness with family income for the subsample of the 2014 GSS that identified themselves as Jewish.(a) Give an example of a (i) concordant pair, (ii) discordant pair.(b) The table has 204 concordant pairs and 55 discordant pairs. Find gamma, and interpret.(c) Show how
Explain what is wrong with the interpretation “The probability that liberal Democrats favor legalized gay marriage is 15.1 times the probability that conservative Republicans favor legalized gay marriage.”Give the correct interpretation.(b) For those born after 1980, the odds of favoring
According to a 2015 study by the Pew Research Center (www.people-press.org), the percentage of Americans who favor allowing gays and lesbians to marry legally was 81% for Democrats who identified themselves as liberal and 22% for Republicans who identified themselves as conservative.(a) The odds
Give an example of three variables for which you expect β = 0 in the model E(y) = α + βx1 but for which it is plausible that β1 = 0 in the model E(y) = α + β1x1 + β2x2.
Refer to Table 8.1 (page 228) on political party ID and gender. Find and interpret the odds ratio for each 2×2 subtable. Explain why this analysis suggests that the last two columns show a very weak association.
According to the U.S. Bureau of Justice Statistics, in 2014 the incarceration rate in the nation’s prisons was 904 per 100,000 male residents, 65 per 100,000 female residents, 2805 per 100,000 black residents, and 466 per 100,000 white residents. (Source: www.bjs.gov.)(a) Find the odds ratio
The 2012 National Survey on Drug Use and Health(NSDUH) estimated that 23% of Americans aged 12 or over reported binge drinking in the past month, and 7%had used marijuana in the past month.(a) Find the odds of (i) binge drinking, (ii) marijuana use.Interpret.(b) Find the odds ratio comparing binge
Table 8.24 cross-classifies 68,694 passengers in autos and light trucks involved in accidents in the state of Maine by whether they were wearing a seat belt and by whether they were injured or killed. Describe the association using(a) The difference between two proportions, treating whether injured
In a survey of senior high school students inDayton, Ohio, 1449 students had used both alcohol and cigarettes, 281 had used neither, 500 had used alcohol but not cigarettes, and 46 had used cigarettes but not alcohol.(a) Construct the 2 × 2 table relating alcohol use to cigarette use. Describe the
For the models E(y) = α + βx and E(y) =α + β1x1 + β2x2, express null hypotheses in terms of correlations that are equivalent to the following:(a) H0: β = 0.(b) H0: β1 = β2 = 0.
In a recent GSS, the death penalty for subjects convicted of murder was favored by 74% of whites and 43%of blacks. It was favored by 75% of males and 63% of females.In this sample, which variable was more strongly associated with death penalty opinion—race, or gender?Explain why.
A report by the Gallup organization in February 2015 estimated that 9% of Republicans approved of President Barack Obama’s performance, whereas 79% of Democrats approved.Would you characterize the association between political party affiliation and opinion about Obama’s performance as weak, or
Table 8.23, from the 2014 General Social Survey, cross-classifies happiness and marital status.(a) Software reports that X2 = 135.3.Interpret.(b) The table also shows, in parentheses, the standardized residuals. Summarize the association by indicating which marital statuses have strong evidence of
For a 2×4 cross-classification of gender and religiosity(very, moderately, slightly, not at all) for recent GSS data, the standardized residual was 3.2 for females who are very religious, −3.2 for males who are very religious,−3.5 for females who are not at all religious, and 3.5 for males who
Table 8.22 shows SPSS analyses with the 2014 General Social Survey, for variables party ID and race.(a) Report the expected frequency for the first cell, and show how SPSS obtained it.(b) Test the hypothesis of independence. Report the test statistic and P-value, and interpret.(c) Use the
The sample in Table 8.16 is 382 black Americans.Table 8.21 shows cell counts and standardized residuals for income and happiness for white subjects in the 2014 General Social Survey.(a) Interpret the Pearson chi-squared statistic and its P-value.(b) Interpret the standardized residuals in the four
In the GSS, subjects who were married were asked the happiness of their marriage, the variable coded as HAPMAR.(a) Go to sda.berkeley.edu/GSS/ and construct a contingency table for 2014 relating HAPMAR to family income measured as (above average, average, below average), by entering FINRELA(r: 1-2;
11.57.*Whenever x1 and x2 are uncorrelated, then R2 for the model E(y) = α+β1x1+β2x2 satisfies R2 = r2 yx1+r2 yx2 .In this case, draw a figure that portrays the variability in y, the part of that variability explained by each of x1 and x2, and the total variability explained by both of them
Are people happier who believe in life after death?Go to the GSS website sda.berkeley.edu/GSS and download the contingency table for the 2014 survey relating happiness and whether you believe in life after death(variables HAPPY and POSTLIFE, with YEAR(2014) in the selection filter).(a) State a
Table 8.20 is based on results described in a study5 that examined the effects of alcohol consumption and drug use on sexual behavior, for undergraduate students at a university in the southeastern United States. In this table, the columns refer to whether the student engaged in unprotected sex in
In 2010, the GSS asked about willingness to accept cuts in the standard of living to help the environment, with categories (very willing, fairly willing, neither willing nor unwilling, not very willing, not at all willing). When this was cross tabulated with sex, X2 = 3.3.(a) What are the
A sociologist uses a 2 × 4 contingency table to compare four groups on a binary response variable. For group i, let πi denote the population proportion of response in the first outcome category, i = 1, 2, 3, 4. Explain what df = 3 means in the context of comparing these four population
How large a X2 value provides a P-value of 0.05 for testing independence for the following table dimensions?(a) 2 × 2 (b) 3 × 3 (c) 2 × 5 (d) 5 × 5(e) 3 × 9
Data posted at the FBI website (www.fbi.gov) indicated that of all blacks slain in 2013, 92% were slain by blacks, and of all whites slain in 2013, 93% were slain by whites. Let y denote race of victim and x denote race of murderer.(a) Which conditional distributions do these statistics refer to,
11.58.* Which of the following sets of correlations would you expect to yield the highest R2-value? Why?(a) ryx1= 0.4, ryx2= 0.4, rx1x2= 0.0.(b) ryx1= 0.4, ryx2= 0.4, rx1x2= 0.5.(c) ryx1= 0.4, ryx2= 0.4, rx1x2= 1.0.
Based on current estimates of how well mammograms detect breast cancer, Table 8.19 shows what to expect for 100,000 adult women over the age of 40 in terms of whether a woman has breast cancer and whether a mammogram gives a positive result (i.e., indicates that the woman has breast cancer).(a)
TheWorld Values Survey4 asked, “How often do you pray?” The response never was given by 16.5% of the 2232 respondents in the United States, by 48.4% of the 1189 respondents in Spain, and by 56.8% of the 1206 respondents in Sweden. Show how to construct a contingency table relating the outcome
A March 2015 survey by the Pew Research Center(www.pewresearch.org) compared various groups of Americans in terms of their support for legalizing marijuana.In considering age groups, it estimated that legalization was supported by 68% of those of age between 18 and 34, by 51% of those of age
Whether a woman becomes pregnant in the next year is a categorical variable with categories (yes, no), and whether she and her partner use contraceptives is another categorical variable with categories (yes, no). Would you expect these variables to be statistically independent, or associated?
GSS surveys routinely show that in the United States, about 40% of males and 40% of females believe that a woman should be able to get an abortion if she wants it for any reason.(a) Construct a contingency table showing the conditional distribution on whether unrestricted abortion should be legal
11.59.* Suppose the correlation between y and x1 equals the multiple correlation between y and x1 and x2. What does this imply about the partial correlation ryx2·x1?Interpret.
The Wilcoxon test differs from parametric procedures comparing means in the sense that(a) It applies directly to ordinal as well as interval response variables.(b) It is unnecessary to assume that the population distribution is normal.(c) Random sampling is not assumed.7.65.* A test consists of 100
To compare the population mean annual incomes for Hispanics (μ1) and for whites (μ2) having jobs in construction, we construct a 95% confidence interval forμ2 − μ1.(a) If the confidence interval is (3000, 6000), then at this confidence level we conclude that the population mean income is
A99% confidence interval for the difference π2−π1 between the proportions of men and women in California who are alcoholics equals (0.02, 0.09).(a) We are 99% confident that the proportion of alcoholics is between 0.02 and 0.09.(b) We are 99% confident that the proportion of men in California
11.60.* Software reports four types of sums of squares in multiple regression models. The Type I sum of squares, sometimes called sequential SS, represents the variability explained by a variable, controlling for variables previously entered into the model. The Type III sum of squares, sometimes
True or false? If you know the standard error of the sample mean for each of two independent samples, you can figure out the standard error of the difference between the sample means, even if you do not know the sample sizes.In Exercises 7.62–7.64, select the correct response(s). More than one
True or false? If a 95% confidence interval for(μ2 − μ1) contains only positive numbers, then we can conclude that both μ1 and μ2 are positive.
An AP story about a University of Chicago survey of 1600 people of ages 15 to 25 in several Midwest U.S.cities indicated that 58% of black youth, 45% of Hispanic youth, and 23% of white youth reported listening to rap music every day.(a) True or false: If a 95% confidence interval comparing the
Describe a situation in which it would be more sensible to compare means using dependent samples than independent samples.
A pool of six candidates for three managerial positions includes three females and three males. Table 7.31 shows the results.(a) Denote the three females by F1, F2, and F3 and the 3 males by M1, M2, and M3. Identify the 20 distinct samples of size three that can be chosen from these six
A survey by the Harris Poll of 2250 Americans in 2013 indicated that 42% believe in ghosts, 26% believe in witches, 29% believe in astrology, and 36% believe in creationism.(a) Is it valid to compare the proportions using inferential methods for independent samples? Explain.(b) Doyou have enough
From Example 6.4 (page 160), for the cognitive behavioral therapy group the sample mean change in weight of 3.0 pounds was significantly different from 0. However, Example 7.8 (page 206) showed it is not significantly different from the mean change for the control group, even though that group had
Table 7.30 compares two hospitals on the outcomes of patient admissions for severe pneumonia. Although patient status is an ordinal variable, two researchers who analyze the data treat it as an interval variable. The first researcher assigns the scores (0, 5, 10) to the three categories.The second
The International Adult Literacy Survey21 was a 22-country study in which nationally representative samples of adults were interviewed and tested at home, using the same literacy test having scores that could range from 0 to 500. For those of age 16–25, some of the mean prose literacy scores were
In 2011, the United States Supreme Court dealt with a sex discrimination case in which women managers at Walmart earned $14,500 a year less, on the average, than their male counterparts. If you were also given the standard errors of the annual mean salaries for male and female managers at Walmart,
11.61.* Adjusted R2 is defined as R2 adj= 1 − s2 s2y, where s2 is the estimated conditional variance and s2y is the sample variance of y, both of which are unbiased. This relates to ordinary R2 by R2 adj= R2 −p n − (p + 1)(1 − R2).(a) Suppose R2 = 0.339 for a model with p = 2 explanatory
In the World Values Survey, interviews of 1902 subjects in the Netherlands found that 29.2% reported having confidence in the European Union and 33.0% reported having confidence in the government of the Netherlands.Do you have enough information to make an inferential comparison of the percentages?
The results in Table 7.29 are from a study20 of physical attractiveness and subjective well-being. A sample of college students were rated by a panel on their physical attractiveness. The table presents the number of dates in the past three months for students rated in the top or bottom quartile of
The World Values Survey asks if homosexuality is justifiable, on a scale from 1 (“never”) to 10 (“always”).In 1981–1984 surveys, the 2325 respondents in the United States had a mean response of 2.4 and standard deviation of 2.3.In 2010–2014 surveys, the 2232 U.S. respondents had a mean
According to an article in The New York Times (December 6, 2015), the number of annual gun homicides per million people is 31.2 in the United States, 5.6 in Canada, 2.3 in the Netherlands, 0.9 in England, and 0.1 in Japan.Show an informative way to compare these rates between the United States and
A study19 considered whether greater levels of TV watching by teenagers were associated with a greater likelihood of committing aggressive acts over the years. The researchers randomly sampled 707 families in two counties in northern New York State and made follow-up observations over 17 years.
Browse one or two daily online newspapers such as The New York Times. Find an article about a research study that compared two groups. Prepare a short report that answers the following questions:(a) What was the purpose of the research study?(b) Identify explanatory and response variables.(c) Can
Pose null and alternative hypotheses about the relationship between time spent on the Internet (variable WWWHR for the GSS) and a binary explanatory that you believe may be associated with Internet use. Using the most recent GSS data on these variables at sda.berkeley.edu/GSS, conduct the test.
Exercise 3.6 on page 70 showed data on carbon dioxide emissions, a major contributor to global warming, for advanced industrialized nations. State a research question for these data that involves comparing means or proportions. Conduct an investigation to answer this question.
Using the Comparing Two Means applet at www.pearsonglobaleditions.com/Agresti, construct two scenarios of independent samples of four men and four women with y = number of hours spent on Internet in past week having ¯y1 = 5 and ¯y2 = 10, such that for testing H0: μ1 = μ2 against Ha: μ1 = μ2,
For the data file created in Exercise 1.12, with variables chosen by your instructor, state a research question and conduct inferential statistical analyses. Prepare a report that summarizes your findings. In this report, also use graphical and numerical methods to describe the data.
For the Students data file (Exercise 1.11 on page 21), use graphical and numerical summaries and inferential statistical methods for the following:(a) Compare political ideology of students identifying as Democrats and as Republicans.(b) Compare opinions of males and females about legalized
In a study about lesbianism, 45 young adults were asked whether they had ever had a same-gender sexual relationship. Table 7.28 shows results. Use software to test whether the probability of this is higher for those raised by lesbian mothers. Interpret.TABLE 7.28 Same-Gender Relationship Mother Yes
An experimental study18 of young children’s moral behavior used as subjects 32 three-year-old girls, half assigned to each of two conditions. Each girl and two actors created a picture or clay sculpture, after which one actor left the room. In the Harm condition, the remaining actor then
The World Values Survey has asked if homosexuality is justifiable, on a scale from 1 (“never”) to 10 (“always”).In 1981–1984 surveys in the United States of 2325 subjects, 62.4% gave response 1. In 2010–2014 surveys of 2232 respondents, 24.0% gave response 1. A report claimed that this
A General Social Survey asked subjects their opinions about government spending on health and on law enforcement. Table 7.26 shows results.(a) Find the sample proportion favoring increased spending, for each item.(b) Test whether the population proportions are equal.Report the P-value, and
11.62.* Let R2y(x1,... xp) denote R2 for the multiple regression model with p explanatory variables. Explain why r2 yxp·x1,...,xp−1=R2y(x1,...,xp)− R2y(x1,...,xp−1)1 − R2y(x1,...,xp−1)
Recent years have seen impressive improvements in systems for automatically recognizing speech. Research in comparing the quality of different speech recognition systems often uses as a benchmark test a series of isolated words, checking how often each system makes errors recognizing the word.
Two new short courses have been proposed for helping students who suffer from severe math phobia, scoring at least 8 on a measure of math phobia that falls between 0 and 10 (based on responses to 10 questions). A sample of 10 such students were randomly allocated to the two courses. Following the
In 2014, the General Social Survey asked about the number of hours a week spent on the World Wide Web, not counting e-mail. The 778 females had a mean of 11.2 and standard deviation of 13.7.The 620 males had a mean of 11.9 and standard deviation of 16.0.Use these results to make an inference
For the survey of students described in Exercise 1.11, the responses on political ideology had a mean of 3.18 and standard deviation of 1.72 for the 51 nonvegetarian students and a mean of 2.22 and standard deviation of 0.67 for the 9 vegetarian students. When we use software to compare the means
.11.63.* The numerator R2 – r2 yx1 of the squared partial correlation r2 yx2·x1 gives the increase in the proportion of explained variation from adding x2 to the model. This increment, denoted by r2 y(x2·x1), is called the squared semipartial correlation. One can use squared semipartial
A study16 of treatments for obesity for rural women examined the impact of a six-month behavioral weight loss program delivered by phone either one-on-one with a counselor or to a group via conference call. A sample of rural women classified as obese by their BMI were randomly assigned to the two
Refer to the previous exercise. To avoid bias from the samples being unbalanced with such small n, the psychologist redesigned the experiment. She forms three pairs of subjects, such that the patients matched in any given pair are similar in health and socioeconomic status.For each pair, she
Aclinical psychologist wants to choose between two therapies for treating mental depression. For six patients, she randomly selects three to receive therapy A, and the other three receive therapy B. She selects small samples for ethical reasons; if her experiment indicates that one therapy is
Refer to the previous exercise. For comparing parties and sports, software reports a 95% confidence interval of (−3.33, 28.93) and a P-value of 0.106.Explain the connection between the results of the significance test and the confidence interval.
As part of her class project, a student at the University of Florida randomly sampled 10 fellow students to investigate their most common social activities. As part of the study, she asked the students to state how many times they had done each of the following activities during the previous year:
In a study15 of the effect of the compound tomoxetine as a treatment for adult attention deficit hyperactivity disorder (ADHD), the 21 subjects had an ADHD rating scale mean of 30.0 (s = 6.7) at baseline and 21.5 (s = 10.1)after three weeks of treatment. The standard deviation was 9.84 for the 21
In a study comparing various drink types (tea, energy drink, coffee with cream, lime soda, etc.) on teenagers’desire for additional drinks after various lengths of time, coffee with cream had the least effect. In one analysis for coffee with cream, the researchers reported that desire ratings
For a 2015 study, Table 7.19 shows software output for evaluating the number of hours of Internet surfing per day by age.(a) Interpret the reported confidence interval. Can you conclude that one population mean is higher? If so, which one? Explain.(b) Interpret the reported P-value.(c) Explain the
A survey for 2016, comparing retired and in-service persons on the number of hours a day that they spent on gardening, gave----------------------------------------------Group n Mean StdDev Std Error Mean Retired 875 4.65 1.80 0.073 In-service 525 2.75 1.47
A current employees’ behavior survey asked, “How many days in the past 15 days have you felt demotivated?”Software reported sample means of 5.9 for executives and 2.1 for nonexecutives, with a 95% confidence interval comparing them of (1.5, 3.2), a t statistic of 5.2, and a P-value of
In Great Britain, the Time Use Survey14 studied how a random sample of Brits spend their time on a typical day. For those who reported working full time, Table 7.18 reports the mean and standard deviation of the reported average number of minutes per day spent on cooking and washing up.TABLE 7.18
A study evaluated the degree of addiction that children form to cartoon shows once they start watching them in their leisure hours. The study used a random sample of 445 school students in two metropolitan cities who had started watching cartoon shows by the commencement of the study. The response

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