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nonparametric statistical inference

Statistical Methods For The Social Sciences 4th Edition Barbara Finlay, Alan Agresti - Solutions

9.4. The OECD (Organization for Economic Cooperation and Development) consists of 20 advanced, industrialized countries. For these nations,4 the prediction equation relatingy = child poverty rate in 2000 to x = social expenditure as a percent of gross domestic product is y = 22 — 1.3x. The
9.3. Anthropologists often try to reconstruct information using partial human remains at burialsites. For instance, after finding a femur (thighbone), they may want to predict how tall an individual was. An equation they use to do this is y = 61.4 + 2.4x, where y is the predicted height and x is
9.2. Sketch plots ofthe following prediction equations, for values ofx between 0 and 10:(a) y = 7 + 0.5x(b) y = 7 + x(c) y = 1 - x(d) y = 7 - 0.5x(e) y = 7(f) y = x
8.45. For a 2 X 2 table with cell counts a,b,c,d, the sample log odds ratio Iog0 has approximately a normal sampling distribution with estimated standard error= ,/i + |+ l+l.v n h c d The antilogs of the endpoints of the confidence interval for log(0) are endpoints of the confidence interval for 6.
*8.44. A chi-squared variable with degrees of freedom equal to df has representation z\ + ... + z 2df, where z i,...,Zdf are independentstandard normal variates.(a) If z is a test statistic that has a standard normal distribution, what distribution does z 2have?(b) Explain how to get the
8.43. Construct a 3 x 3 table for each of the following conditions:(a) Gamma equals 1. {Hint: There should be no discordant pairs.)(b) Gamma equals-1.(c) Gamma equals 0.
8.42. For 2X2 tables, gamma simplifies to a measure first proposed about 1900 by the 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,h) in row I and {c,d) in row 2, the number of concordant
*8.41. Table 8.33 exhibits the maximum possible association between two binary variables for a sample of size n.(a) Show that y 2= n for this table and, hence, that the maximum value of y 2for 2X2 tables is n.
8.40. 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 ofsingle-parent
8.39. 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 rcsponsc(s))(a) The statistic actually treats the variables as nominal.Information about the ordering is
8.38. 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 x 2 test statistic and a very small P-value for testing
8.37. (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 P-valucs not necessarily referring to an important effect apply for any
8.36. Shortly before a gubernatorial election, a poll asks a random sample of 50 potential voters the following questions:Do you consider yourself to be a Democrat(D). a Republican (R), or Independent (I)?If you were to vote today, would you vote for the Democratic candidate (D), the
8.35. A study3 of American armed forces who had served in Iraq or Afghanistan found that the event of being attacked or ambushed was reported by 1139 of 1961 Army members who had served in Afghanistan. 789 of 883 Army members who had served in Iraq, and 764 of 805 Marines who had served in Iraq.
8.34. For 2006 GSS data, of those identifying as Democrats, 616 classified themselves as liberal and 262 as conservative. Of those identifying as Republicans, 94 called themselves liberal and 721 called themselves conservative. Using methods presented in this chapter, describe the strength of
8.33. Several sociologists have reported that racial prejudice varies according to religious group. Examine this using Table 8.30, for white respondents to the 2002 GSS. The variables are Fundamentalism/Liberalism of Respondent's Religion (FUND)and response to the question (RACMAR), "Do you think
8.32. Pose a research question about attitude regarding homosexual relations and political ideology. Using the most recent GSS data on HOMOSEX and POLVIEWS, conduct a descriptive and inferential analysis to address this question. Prepare a short report summarizing your analysis.
8.31. In 2002 the GSS asked how housework was shared between the respondent and his or her spouse(HHWKFAIR). 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 = 1 do a bit less than my fair share, 5 = 1 do much
8.30. 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.
8.29. Refer to the "Student survey" data file (Exercise 1.11 on pageS). Using software, create and
8.28. Refer to Exercise 8.13, on happiness and income.The analysis there does not take into account the ordinality of the variables. Using software:(a) Summarize the strength of association by finding and interpreting gamma.(b) Construct and interpret a 95% confidence interval for the population
8.27. A study on educational aspirations of high school students2 measured aspirations using the scale(some high school, high school graduate, some college, college graduate) and family income with three ordered categories. Software provides the results shown in Table 8.28.(a) Use gamma to
8.26. For the 2006 GSS, y = 0.22 for the relationship betweenjob satisfaction (SATJOB; categories very dissatisfied, little dissatisfied, moderately satisfied, very satisfied) and family income (FINRELA;below average, average, above average).(a) Would you consider this a very strong or relatively
8.25. Table 8.27 cross-classifies happiness with family income for the subsample of the 2004 GSS that identified themselves as Jewish.(a) Find the number of (i) concordant pairs,(ii) discordant pairs.(b) Find gamma and interpret.TABLE 8.27 HAPPY Not_too Pretty Very 12 1 0 5 2 2 4 0(c) Show how to
8.24. For college freshmen in 2004, the percent who agreed that homosexual relationships should be legally prohibited was 38.0% of males and 23.4%of females (www.gseis.ucla.edu/heri/american_ frcshman.html).(a) The odds ratio is 2.01. Explain what is wrong with the interpretation, "The probability
8.23. Refer to Table 8.1 (page 222) on political party ID and gender. Find and interpret the odds ratio for each 2x2 subtable. Explain why this analysis suggests that the last two columns show essentially no association.
8.21. According to the Substance Abuse and Mental Health Archive, a 2003 national household survey on drug abuse indicated that for Americans aged 8.22. According to the U.S. Department of Justice, in 2004 the incarceration rate in the nation's prisons was 1 per 109 male residents, 1 per 1563
8.20. Table 8.26 cross-classifies 68,694 passengers in autos and light trucks involved in accidents in the state of Maine by whether they were wearing a scat belt and by whether they were injured or killed. Describe the association using(a) The difference between two proportions, treating whether
8.19. Referto Exercise 8.10, on alcohol use and cigarette use.(a) Describe the strength of association using the difference between users and nonusers of alcohol in the proportions who have used cigarettes. Interpret.(b) Describe the strength of association using the difference between users and
8.18. 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% offemales. In this sample, which variable was more strongly associated with death penalty opinion—race or gender? Explain why.
8.17. In a USA TodayIGaWup poll in July 2006, 82%of Republicans approved of President George W.Bush's performance, whereas 9% of Democrats approved. Would you characterize the association between political party affiliation and opinion about Bush's performance as weak, or strong?Explain why.
8.16. Table 8.25 is from the 2006 General Social Survey, cross-classifying happiness (HAPPY) and marital status (MARITAL).TABLE 8.25 Marital Very Pretty Not Too Status Happy Happy Happy Married 600(13.1) 720 (-5.4) 93 (-10.0)Widowed 63 (-2.2) 142 (-0.2) 51 (3.4)Divorced 93 (-6.1) 304(3.2) 88
8.15. For a 2 X 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
8.14. Table 8.24 shows SPSS analyses with the 2004 GSS, 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 between party ID and race. Report the test statistic and P-valuc and interpret.(c) Use
8.13. The sample in Table 8.15 is 157 black Americans. Table 8.23 shows cell counts and standardized residuals for income and happiness for white subjects in the 2004 GSS.(a) Explain how to interpret the Pearson chisquarcd statistic and its associated F-valuc.(b) Explain how to interpret the
8.12. In the GSS. subjects who were married were asked the happiness oftheir marriage, the variable coded as HAPMAR.(a) Go to sda.berkeley.edu/GSS/ and construct a contingency table for 2006 relating HAPMAR to family income measured as (above average, average, below average), by entering FINRELA(r:
8.11. Are people happier who believe in life after death?Go to the GSS Web site sda.berkeley.edu/GSS and download the contingency table forthe 2006 survey relating happiness and whether you believe in life after death (variables HAPPY and POSTLIFE, with YEAR(2006) in the 'selection filter').(a)
8.10. Table 8.22 refers to a survey of senior high school students in Dayton, Ohio.(a) Construct conditional distributions that treat cigarette smoking as the response variable. Interpret.(b) Test whether cigarette use and alcohol use are statistically independent. Report the E-value and
8.9. In 2000 the GSS asked whether a subject is willing to accept cuts in the standard of living to help the environment (GRNSOL), with categories (very willing, fairly willing, neither willing nor unwilling, not very willing, not at all willing). When this was cross-tabulated with sex, x 2-
8.7. How large a x 2value provides a E-value of 0.05 for testing independence for the following table dimensions?a) 2 x 2b) 3 x 3c) 2 x 5d) 5 x 5e) 3 X 9 8.8. Show that the contingency table in Table 8.21 has four degrees of freedom by showing how the four cell counts given determine the
8.6. Data posted at the FBI Web site (www.fbi.gov)indicated that of all blacks slain in 2005, 91% were slain by blacks, and of all whites slain in 2005,83%
8.5. Based on current estimates of how well mammograms detect breast cancer. Table 8.20 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)
8.4. Some political analysts claimed that during the presidency of George W. Bush, the popularity of the U.S. decreased dramatically around the world. In America Against the World: How We Are Different and Why We Are Disliked} the Pew Research Centersummarized results of91,000 interviews conducted
8.3. Every year, a large-scale poll of college freshmen conducted by the Higher Education Research Institute at UCLA asks their opinions about a variety of issues. In 2002, 46% of men and 35% of women in the survey of 283,000 college freshmen indicated support for legalization of marijuana.(a) If
8.2. Whether a woman becomes pregnant in the next year is a categorical variable with categories (yes, no), and whethershe and herpartner use contraceptives is another categorical variable with categories(yes, no). Would you expect these variables to be statistically independent, or associated?
8.1. GSS surveys routinely show that in the United States, about 40% of males and 40% of females believe that a women should be able to get an abortion if she wants it for any reason (variable ABANY).(a) Construct a contingency table showing the conditional distribution on whether unrestricted
7.65. A test consists of 100 true-false questions. Joe did not study, so on each question, he randomly *7.66.guesses the correct response.(a) Find the probability that he scores at least 70, thus passing the exam. (Hint: Use the sampling distribution for the proportion of correct responses.)(b)
7.64. The Wilcoxon test differs from parametric procedures (for means) in the sense that(a) It applies directly to ordinal as well as interval response variables.
7.63. To compare the population mean annual incomes for Hispanics (^1) and for whiles (1x2) having jobs in construction, we construct a 95% confidence interval for fX2 — fx\.(a) If the confidence interval is (3000, 6000), then at this confidence level we conclude that the population mean income
7.62. A 99% confidence interval for the difference 772 - T 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 arc 99% confident that the proportion of men in
7.61. True or false? If you know the standard error of the sample mean for each oftwo 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, selectthe correctresponse(s). More than one
7.60. True or false? If a 95% confidence interval for(A2 — Mi) contains only positive numbers, then we can conclude that both /xi and 1x2 are positive.
7.59. An Associated Press story (Feb. 1, 2007) 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%
7.58. Describe a situation in which it would be more sensible to compare means using dependent samples than independent samples.
7.57. A pool ofsix candidates for three managerial positions includes three females and three males. Table 7.26 shows the results.(a) Denote the three females by F\, F2, E3 and the three males by M\, M2. M3. Identify the 20 distinct samples of size three that can be chosen from these six
7.55. From Example 6.4 (page 151) in Chapter 6, for the cognitive behavioral therapy group the sample mean change in weight of 3.0 pounds was significantly different from 0. However, Example 7.7(page 198) showed it is not significantly different from the mean change for the control group, even
7.54. Table 7.25 compares two hospitals on the outcomes of patient admissions forsevere 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
7.53. The International Adult Literacy Survey(www.nifl.gov/nifl/facts/lALS.html) 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 0-500. For those of age 16-25, some
7.52. A Time Magazine article titled "Wal-Mart's Gender Gap" (July 5, 2004) stated that in 2001 women managers at Wal-Mart earned $14,500 a year less, on the average, than their male counterparts. Ifyou were also given the standard errors of the annual mean salaries for male and female managers at
7.51. A report (12/04/2002) by the Pew Research Center on What the World Thinks in 2002 reported that"the American public is strikingly at odds with publics around the world in its views aboutthe U.S.role in the world and the global impact of American actions." Conclusions were based on polls in
7.50. The results in Table 7.24 arc from a study16 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
7.49. A study1"' compared substance use, delinquency, psychological well-being, and socialsupport among various family types,for a sample ofurban AfricanAmerican adolescent males. The sample contained 108 subjects from single-mother households and 44 from households with both biological parents.
7.48. When asked by the GSS about the number of people with whom the subject had discussed matters of importance over the past six months (variable NUMGIVEN), the response of 0 was made by 8.9% of 1531 respondents in 1985 and by 24.6%of 1482 respondents in 2004. Analyze these data inferentially and
7.47. A recent study14 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
7.46. Browse one or two daily newspapers such as The New York Times (hard copy or online). Copy 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
7.45. Pose null and alternative hypotheses about the relationship between time spent on the Internet(WWWHR for the GSS) and a binary predictor available atthe GSSthat you believe may be associated with Internet use. Using the most recent GSS data on these variables at sda.berkeiey.edu/GSS, conduct
7.44. Exercise 3.6 in Chapter 3 on page 61 showed data on carbon dioxide emissions, a major contributor to global warming, for advanced industrialized nations. Is there a difference between European and non-European nationsin their emission levels?Conduct an investigation to answer this question.
7.43. 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 reportthatsummarizes yourfindings.In this report, also use graphical and numerical methods to describe the data and, if
7.42. Using software with the student survey data set(Exercise 1.11), construct a confidence interval and conduct a test:(a) To compare males and females in terms of opinions about legalized abortion. Interpret.(b) To compare the mean weekly time spent watching TV to the mean weekly time in sports
7.40. Refer to the previous problem. The young adults were also asked whether they had ever had a same-gender sexual relationship. Table 7.23 7.41. For the "Student survey" data file (Exercise 1.11 on page 8), compare political ideology ofstudents identifying with the Democratic party and with the
7.38. A study12 used data from the Longitudinal Study of Aging to investigate how older people's health and social characteristics influence how far they 7.39. A study13 investigated the sexual orientation of adults who had been raised as children in lesbian families. Twcntj'-fivc children of
7.37. A GSS asked subjects their opinions about governmentspending on health and governmentspending on law enforcement. For each, should it increase, or should it decrease? Table 7.20 shows results.(a) Find the sample proportion favoring increased spending, for each item.(b) Test whether the
7.35. Two new short courses have been proposed for helping students who suffer from severe math phobia, scoring at least 8 on a measure ofmath phobia that falls between 0 and 10 (based on responses to?7.36. A GSS asked subjects whether they believed in heaven and whether they believed in hell. Of
7.34. In 2006, the GSS asked about the number of hours a week spent on the World Wide Web (WWWTIME). The 1569 females had a mean of 4.9 and standard deviation of 8.6. The 1196 males had a mean of 6.2 and standard deviation of 9.9. Use these resultsto make an inference comparing males and females on
7.32. A study11 of bulimia among college women considered the effect of childhood sexual abuse on various components of a Family Environment Scale. For a measure of family cohesion, the sample mean for the bulimic students was 2.0 for 13 sexually abused students and 4.8 for 17 nonabuscd
7.31. Refer to the previous exercise. To avoid bias from the samples being unbalanced with such small n, the psychologist redesigned the experiment. She?
7.30. A clinical 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
7.29. Refer to the previous exercise. For comparing partics and sports, software reports a 95% confidence interval of (-3.33,28.93) and a P-value of 0.106.(a) Interpret the P-value.(b) Explain the connection between the results of the test and the confidence interval.
7.28. As part of her class project, a student atthe University ofFlorida randomly sampled 10 fellow students to investigate their most common social activities.As part ofthe study, she asked the students to state how many times they had done each of the following activities during the previous
7.27. A paired-difference experiment"1 dealing with response latencies for noise detection under two conditions used a sample of twelve 9-month-old children and reported a sample mean difference of 70.1 and standard deviation of 49.4 for the differences. In their discussion, the authors reported a
7.26. A study9 compared personality characteristics between adult children of alcoholics and a control group matched on age and gender. For the 29 pairs of women, the authors reported a mean of 24.8 on the well-being measure for the children of alcoholics, and a mean of 29.0 for the control group.
7.25. For the 2004 GSS, Table 7.15 shows software output for evaluating the number of hours of TV watching per day by race.TABLE 7.15 Race N Mean StDev SE Mean Black 101 4.09 3.63 0.3616 White 724 2.59 2.31 0.0859 Difference = mu (Black) - mu (White)Estimate for difference : 1.50 957, CI for
7.24. For the 2006 GSS, a comparison of females and males on the number of hours a day that the subject watched TV gave:Group N Mean StDev SE Mean Females 1117 2.99 2.34 0.070 Males 870 2.86 2.22 0.075(a) Conduct all parts of a significance test to analyze whether the population means differ for
7.23. A recent GSS asked, "How many days in the past 7 days have you felt sad?" Software reported sample means of 1.8 for females and 1.4 for males, with a 95% confidence interval comparing them of (0.2, 0.6), a t statistic of 4.8, and a R-value of 0.000.Interpret these results.
7.22. Refer to Exercise 7.17, on compulsive buying behavior. The total credit card balance had a mean of $3399 and standard deviation of $5595 for 100 compulsive buyers and a mean of $2837 and standard deviation of $6335 for 1682 other respondents.(a) Estimate the difference between the means for
7.21. A 30-month study evaluated the degree of addiction that teenagers form to nicotine once they begin experimenting with smoking.8 The study used a random sample of 332 seventh-grade students in two Massachusetts cities who had ever used tobacco by the start ofthe study. The response variable
7.20. Table 7.14 summarizes the number of hours spent in housework per week by gender, based on the 2002 GSS (variable RHHWORK).(a) Estimate the difference between the population means for women and men.(b) Show that the estimated standard error of the sample difference is 0.81. Interpret.(c) Show
7.19. A GSS reported that the 486 females had a mean of 8.3 close friends (s = 15.6) and the 354 males had a mean of 8.9 close friends (.s = 15.5).(a) A 95% confidence interval for the difference between the population means for males and for females is (-1.5, 2.7). Interpret.(b) For each sex, does
7.18. Table 7.13 shows results from a recent General Social Survey on two variables, sex and whether one believes in an afterlife (AFTERLIF). Conduct all steps of a significance test, using a = 0.05, to compare the population proportions of females and males who would respond yes to belief in an
7.17. A study of compulsive buying behavior (uncontrolled urges to buy) conducted a national telephone survey in 2004 of adults ages 18 and over.7 Of 800 men, 44 were judged to be compulsive buyers according to the Compulsive Buying Scale. Of 1501 women, 90 were judged to be compulsive buyers.
7.16. In a survey conducted by Wright State University, senior high school students were asked if they had ever used marijuana. Table 7.12 shows software output. Treating these observations as a random sample from the population of interest:(a) State a research question that could be addressed with
7.15. Refer to the previous exercise on a woman'srole. In 2004, of 411 male respondents, 153 (37.2%) replied yes. Of 472 female respondents, 166 (35.2%)replied yes.(a) Set up notation and specify hypotheses for the hypothesis of no difference between the population proportions of males and of
7.14. Table 7.11 summarizes responses from General Social Surveys in 1977 and in 2006 to the question (FEFAM), "It is much better for everyone involved if the man is the achiever outside the home and the woman takes care of the home and family." Let tti denote the population proportion who agreed
7.13. For the Time Use Survey reported in Table 7.1(page 183), of those working full time, 55% of 1219 men and 74% of 733 women reported spending some time on cooking and washing up during a typical day. Find and interpret a 95% confidence interval for the difference in participation rates.
7.12. In the study mentioned in the previous exercise, the percent who said they had engaged in unplanned sexual activities because of drinking alcohol was 19.2% in 1993 and 21.3% in 2001.(a) Specify assumptions, notation, and hypotheses for a two-sided test comparing the corresponding population
7.11. The College Alcohol Study at the Harvard School of Public Health has interviewed random samples of students at 4-year colleges several times since 1993. Of the students who reported drinking alcohol, the percentage who reported that drinking "to get drunk" is an important reason for drinking
7.10. For a random sample of Canadians, 60% indicate approval ofthe prime minister's performance.A similar poll a month later has a favorable rating of 57%. A 99% confidence interval for the change in the population proportions is (— 0.07,0.01).Explain why (a) there may have been no change in
7.9. An Associated Press story (August 7, 2006) about a research study regarding the impact on teens of sexual lyrics in songs reported, "Teens who said they listened to lots of music with degrading sexual messages were almost twice as likely to start having intercourse ... within the following two
7.8. According to the U.S. National Center for Health Statistics, the annual probability that a male between the ages of 20 and 24 is a homicide victim is about 0.00164 for blacks and 0.00015 for whites.(a) Compare these rates using the difference of proportions.(b) Compare these rates using the
7.7. According to the U.S. Department of Justice, in 2002 the incarceration rate in the nation's prisons was 832 per 100,000 male residents, and 58 per 100,000 female residents.(a) Find the relative risk of being incarcerated, comparing males to females. Interpret.(b) Find the difference of

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