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nonparametric statistical inference
Statistical Methods For The Social Sciences 4th Edition Barbara Finlay, Alan Agresti - Solutions
11.14. Table 11.15 comes from a regression analysis of y = number of children in family, x\ = 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
11.13. Refer to the previous two exercises. When we add X3 = percentage of single-parent families to the model, wc get the results in Table 11.14.(a) Report the prediction equation and interpret the coefficient of poverty rate.
11.12. Refer to the previous exercise.(a) Report the F statistic for testing Hq: /Si =(62 = 0, report its df values and P-valuc, and interpret.(b) Show how to constructthe t statistic fortesting Hq: /3i = 0, report its df and P-value for Ha:(Si ^ 0, and interpret.(c) Construct a 95% confidence
11.11. Table 11.13 shows a printout from fitting the multiple regression model to recent statewide data, excluding D.C., on y = violent crime rate (per 100,000 people), xi = poverty rate (percentage with income below the poverty level), and X2 = percent living in urban areas.B Std. Error(Constant)
11.9. Recent UN data from several nations on y = crude birth rate (number of births per 1000 population size), X| = women's economic activity (female labor force as percentage of male), and X2 = GNP(per capita, in thousands of dollars) has prediction equation y = 34.53 — 0.13xi — 0.64x2.(a)
11.8. Referto the previous exercise. Using software with the "Florida crime" data file at the text website:(a) Construct box plots for each variable and scatterplots and partial regression plots between y and each ofx\ and X2. Interpret these plots.(b) Find the prediction equationsforthe (i)
Explain.(b) Figure 11.13 shows a partial regression plot relating y to xi, controlling for X2. Predict the sign that the estimated effect of xi has in the prediction equation y = a + h\X\ + h2X2-Explain.
11.7. Table 9.16 on page 297 showed data from Florida counties on y = crime rate (number per 1000 residents), X| = median income (thousands of dollars), and X2 = percent in urban environment.(a) Figure 11.12 shows a scattcrplot relating y to xj. Predict the sign that the estimated effect of x\ has
11.6. Refer to the previous exercise.(a) Show how to obtain /^-squared from the sums of squares in the ANOVA table. Interpret it.(b) r 2= 0.78 when GDP is the sole predictor.Why do you think K 2does not increase much when cell-phone use is added to the model, even though it is itself highly
11.5. A regression analysis with recent UN data from several nations on y = percentage of people who use the Internet, X| = per capita gross domestic product (in thousands of dollars), and X2 = percentage of people using cell phones has results shown in Table 11.11.(a) Write the prediction
11.4. Use software with the "2005 statewide crime" data file at the text Web site, with murder rate (number of murders per 100,000 people) as the response variable and with percent of high school graduates and the poverty rate (percentage of the population with income below the poverty level) as
11.3. Refer to the previous exercise:(a) For fixed home size, how much would lot size need to increase to have the same impact as a one square foot increase in home size?(b) Suppose house selling prices arc changed from dollars to thousands of dollars. Explain why the prediction equation changes to
11.2. For recent data in Florida on y = selling price of home (in dollars), xi = size of home (in square feet), X2 = lot size (in square feet), the prediction equation is y = —10,536 + 53.8xi + 2.84x2.(a) A particular home of 1240 square feet on a lot of 18,000 square feet sold for $145,000. Find
11.1. For students at Waiden University, the relationship between y = college CPA (with range 0-4.0)and xi - high school CPA (range 0-4.0) and X2 = college board score (range 200-800) satisfies E(y) = 0.20 + O.SO.ri + 0.002x2.(a) Find the mean college GPA for students having (i) high school GPA =
10.45. Consider the relationship between Y = political party preference (Democrat, Republican) and Xi = race (Black, White) and A2 = gender. There is an association between Y and both Xi and X2, with the Democrat preference being more likely for blacks than whites and for women than men.(a) X\ and
10.44. Example 9.10 in the previous chapter used a data set on house sales to regress Y = selling price of home (in dollars) to A = size of house(in square feet). The prediction equation was y = -50,926 + 126.6x. Now we regard size of house as Xi and also consider X2 = whether the house is new (yes
10.42. For all court trials about homicides in Florida between 1976 and 1987, the difference of 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.8 This shows evidence of(a) a spurious association.(b) statistical
10.41. A study (in Adolescence, vol. 335, 2000, p. 445)reported a sample correlation of 0.45 between depression and loneliness and —0.74 between loneliness and self-esteem. True or false: By the chain law, the sample correlation between depression and self esteem was negative.Select the best
10.40. A recent study (in Behavior Modification, vol. 29, 2005, p. 677) reported a correlation of0.68 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
10.39. A study of compulsive buying behavior conducted a national telephone survey in 2004 of adults ages 18 and over.7 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
10.38. Give an example of three variables for which the effect of X\ on Y would be(a) 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 X2 is controlled(d) Unaffected by
10.37. A 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, Table 10.10 shows results.(a) Describe the relationship between mother's employment and GPA for females and for males. Does this
10.34. 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 that women tend to live longer lives now than earlier in this century. How might a comparison of breast cancerrates now with
10.33. 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. Docs this association reflect a causal link between drinking bottled
10.29. 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, Xi = primary language of family, and X2 =
10.28. Suppose that Aj = 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 thing this is more likely to
10.26. For the student survey data (Exercise 1.11), are there any pairs of variables for which you expect the association to disappear under control for a third variable? Explain.10.27. Using the most recent GSS, construct a contingency table relating gender (GSS variable SEX)and party
10.25. Refer to the "Student survey" data file (Exercise 1.11 on page 7). Construct partial tables relating opinion about abortion to opinion about life after death, controlling for attendance at religious services, measured using the two categories, (Never or occasionally. Most weeks or every
10.24. 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 ofstudent was controlled, the gamma measures for the two partial
10.22. For lower-level managerial employees of a fastfood chain, the prediction equation relating Y =annual income (thousands of dollars) to X\ =number of years experience on the job equals y = 14.2 + l.lxi for males and y = 14.2 + 0.4xi for females. Explain how these equations show evidence of
10.21. According to the U.S. Census Bureau, in 2000 the population median income was estimated to be $29,661 for white females, $25,736 for black females, $40,350 for white males, $30,886 for black males. Compare the difference in median incomes between males and females for (a) white subjects(b)
10.19. Table 10.8 relates Y = exam score (1 = below median, 2 = above median) to gender, controlling for subject of exam (Math, Verbal). Show that subject of exam is a suppressor variable.
10.18. Table 10.7 lists the mean salary, in thousands of dollars, of faculty on nine-month contracts in U.S.institutions of higher education in 2003-2004, by gender and academic rank.(a) Suppose that gender is the explanatory variable. Identify the response variable and the control variable.(b)
10.16. For Table 9.16 in Exercise 9.39 on page 297 in Chapter 9, giving countywidc data in Florida for several variables, a moderate positive correlation(r = 0.47) exists between crime rate and percent who are high school graduates. The percentage living in urban areas is also strongly correlated
10.14. In murder trials5 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
10.13. 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? Ifso, describe it.(b) Do the partial tables display
10.12. A study at your university finds that of those who applied to its graduate schoollast year, the percentage admitted was higher for the male applicants than for the female applicants. However, for each department that received applications, the percentage admitted was lower for the male
10.10. A study found that children who eat breakfast get better math grades than those who do not eat breakfast. This result was based on the association between X = whether cat breakfast (yes, no) and Y = grade in last math course taken. How might this result be spurious, and how could you check
10.9. An Associated Press story (February 15, 2002)quoted a study at the University of California at San Diego that reported, based on a nationwide survey, that those who averaged at least 8 hours sleep a night were 12% more likely to die within six years than those who averaged 6.5 to 7.5 hours of
10.8. Figure 9.17 on page 285 of Chapter 9 showed a negative correlation between birth rate and television ownership. Identify a variable to help explain how this association could be spurious.
10.7. Explain what is meant by a spurious association;draw a scatter diagram to illustrate.(a) Illustrate using AT] = shoe size, A^ = age, and y = number of books one has ever read, for children from schools in Winnipeg, Canada.(b) Illustrate using X\ = height, X2 = gender, and y = annual income,
10.6. Explain what it means to control for a variable; use an example to illustrate.
10.5. An association exists between college CPA and whether a college student has ever used marijuana.Explain how(a) The direction of a causal arrow might go in either direction.(b) A third variable might be responsible for the association.
10.4. Cities in the U.S. have a positive correlation between Y = crime rate and X - size of police force. Does this imply that X causes y? Explain.
10.3. For all fires in Chicago last year, data arc available on A = number of firefighters at the fire and y = cost of damages due to the fire. The correlation is positive.(a) Does this mean that having more firefighters at a fire causes the damage to be worse?Explain.(b) Identify a third variable
10.1. State the three criteria for a causal relationship. For each, describe a relationship between two variables that is not causal because that criterion would be violated.
.69. Suppose that the linear regression model E{y) =a + fix with normality and constantstandard deviation a is truly appropriate. Then the interval of numbers Roughly, the correlation is the average crossproduct of the z-score for x times the z-score for y.Using this formula, explain why (a) the
9.68. The values ofy are multiplied by a constantc. From their formulas, show that the standard deviation Sy and the least squares slope b are also then multiplied byc. Thus, show that r = bsx/sy remains the same, so that r docs not depend on the units of measurement.
9.67. Alternative formulas for defining the correlation use terms similar to those in the equation for b:r =- ^)(>' - ^2(* - x)2 l[x(y - y)2 2n - 1/ ,f -\ X - X J y - y \I ^ j'{s y 1
9.65. Refer to the previous exercise. Let p\ and p2 denote the population correlation values between two variables for two separate populations. Let r\ and denote sample values for independent random samples from the populations. To test Hq:Pi =P2' the test statistic is t2 - Ti .t.Z - — with
9.64. A confidence interval for a population correlation p requires a mathematical transformation of r for which the sampling distribution is approximately normal. This transformation is T{r) = (l/2)l0gj(l + r)/(l - r)], where log, denotes the natural (base-e) logarithm. The transformation of the
9.62. A study in 2000 by the National Highway Traffic Safety Administration estimated that 73% of people wearseat belts, that failure to wearseat belts led to 9200 deaths in the previous year, and that that value would decrease by 270 for every 1 percentage point gain in scat belt usage. Let y =
9.61. The slope of the least squares prediction equation and the correlation are similar in the sense that(a) They do not depend on the units.(b) They both must fall between -1 and +1.(c) They both have the same sign.(d) They both equal 1 when there is the strongest association.(e) Their squares
9.59. One can interpret r = 0.30 as follows:(a) A 30% reduction in error occurs in using x to predict y.
9.58. The variables y = annual income (thousands of dollars), X| = number of years of education, and X2 = number of years experience in job arc measured for allthe employees havingcity-fundedjobs, in Knoxville, Tennessee. The following prediction equations and correlations apply.(i.) y = 10 +
9.57. The statistician George Box, who had an illustrious academic career at the University of Wisconsin, is often quoted as saying, "All models arc wrong, but some models are useful." Why do you think that, in practice, (a) all models are wrong, (b) some models are not useful?
9.56. We can regard the problem studied in Chapter 5 of estimating a single mean jx as estimating the parameter in the simple model, E{y) = /x, with a single parameter. Use this fact to explain why the estimate Sy of the standard deviation of the marginal distribution has -n - 1.
9.55. Explain carefully the interpretations of the standard deviations (a) Sy, (b) sx, (c) 5 = square root of MSE, (d) se for h.
9.52. Refer to Exercise 9.39. For these counties, the correlation between high school education rate and median income equals 0.79. Suppose we also have data at the individual level as well as aggregated for a county. Sketch a scatterplot to show that at the individual level, the correlation could
9.51. A study by the Readership Institute7 at Northwestern University used survey data to analyze how reader behavior was influenced by the Iraq war. The response variable was a Reader Behavior Score (RBS), a combined measure summarizing newspaper use frequency, time spent with the newspaper, and
9.50. For a class of 100 students, the teacher takes the 10 students who perform poorest on the midterm exam and enrolls them in a special tutoring program. The overall class mean is 70 both on the midterm and final, but the mean for the specially tutored students increases from 50 to 60. Can we
9.49. Refer to the previous exercise. In view of these assumptions, indicate why such a model would or would not be good in the following situations.(a) x = time, y = percentage unemployed workers in the United States. (Hint: Does this continually tend to increase or decrease?)(b) x = income, y =
9.47. Annual income, in dollars, is an explanatory variable in a regression analysis. For a British version of the report on the analysis, all responses are 9.48. State the assumptions (a) in using the regression equation E{y) = a + fix to represent the relationship between two variables and (b) in
9.46. Describe a situation in which it is inappropriate to use the correlation to measure the association between two quantitative variables.
9.45. Explain why conditional variability can be much less than marginal variability, using the relationship between y = weight and x = age for a sample of boys of ages 2-12, for which perhaps cry = 30 but the conditional cr = 10.
9.44. In 2002, a Census Bureau survey reported that the mean total earnings that a full-time worker in the U.S. can expect to earn between ages 25 and 64 is $1.2 million for those with only a high-school education and $2.1 million for those with a college degree but no advanced degree.(a) Assuming
9.43. The headline of an article in the Gainesville Sun(October 17,2003)stated, "Height can yield a taller paycheck." It described an analysis of four large studies in the U.S. and Britain by a University of Florida professor on subjects' height and salaries.The article reported that for each
9.42. A recent study,6 after pointing out that diets high in fats and sugars (bad for our health) are more affordable than diets high in fruit and vegetables(good for our health), reported, "Every extra 100 g of fats and sweets eaten decreased diet costs by 0.05 to 0.4 Euros, whereas every extra
9.41. Refer to the UN data for several nations shown in Table 9.13 (page 294) and given at the text Web site. Using software, obtain the correlation matrix. Which pairs of variables are highly correlated? Describe the nature of those correlations, and explain how your software handled the missing
9.40. Refer to Table 9.1 (page 256), available in the"statewide crime 2" data set at the text Web site. 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
9.39. Table 9.16 shows data from all 67 Florida counties on crime rate (number of crimes per 1000 residents), median income (in thousands of dollars), percentage of residents with at least a high school education (of those aged at least 25), and the percentage ofthe county's residents living in an
9.38. The Zagat restaurant guides rate each restaurant on a 30-point scale for food, decor, service, and cost. The "Zagat restaurant ratings'" data file at the text Web site shows 2007 ratings for Italian restaurants in Boston, London, and New York. Conduct a correlation analysis to describe the
9.37. Refer to Exercise 3.6 on page 61 of Chapter 3.Pose a research question relating to the association between the percentage ofscats in parliament held by women and female economic activity. Using software, analyze data in Table 3.11 to address this question, and summarize your analyses.
9.34. For the "Student survey" data file (Exercise 1.11 on page 00), conduct regression analyses relating (i) y = political ideology and x = religiosity,(ii) y = high school GPA and x = hours of TV watching. Prepare a report(a) Using graphical ways of portraying the individual variables and their
9.33. For the data for OECD nations in Table 3.11 on page 62, use software to construct a scatterplot relating y = carbon dioxide emissions and x = GDP.(a) Based on this plot, identify a point that may have large influence in determining the correlation. Show that the correlation drops from 0.64 to
9.32. Refer to the previous exercise. When political ideology is regressed on x = number of hours spent in the home on religious activity in the past month (RELHRS1), we obtain B SE B Beta t Sig.Constant 4.0115 0.0422 95.10 0.0000 RELHRS1 0.0064 0.0020 0.087 3.20 0.0015(a) Report and interpret the
9.31. Is political ideology associated with income?When GSS data for 779 cases in 2004 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
9.30. A study was conducted using 49 Catholic female undergraduates at Texas A&M University. The variables measured refer to the parents of these students. The response variable is the number of children that the parents have. One of the explanatory variables is the mother's educational level,
9.29. For 2428 observations from the 2004 GSS on y = number of years of education (EDUC) and x = number ofyears ofmother's education (MAEDUC), y = 10.5 + 0.294x, with i'e = 0.0149.(a) Test the null hypothesis that these variables are independent, and interpret.(b) Find a 95% confidence interval for
9.28. Refer to the previous exercise. Now let the percentage using contraceptives be the explanatory variable for predicting fertility. Using software with the data at the text Web site,(a) Construct a stcm-and-lcaf plot or box plot for fertility, and describe its distribution.(b) Construct a
9.27. Table 9.13, which is the "UN data" file at the text Web site, shows United Nations data from 2005 for several nations on a human development index (HDI, which has components referring to life expectancy at birth, educational attainment, and income per capita), the fertility rate (births per
9.26. Refer to the data at the text Web site, shown in Table 9.16 in Exercise 9.39, giving county-wide data for several variables in Florida. For those data, use software to analyze y = crime rate and x = percentage living in an urban environment.(a) Construct a stem-and-leaf plot and a box plot
9.25. Refer to the "2005 statewide crime" data set at the text Web site. For all 51 observations, use software to analyze the relationship between y = murder rate and x = poverty rate.(a) Construct a scatterplot. Does there seem to be a positive or a negative relationship?(b) Report the prediction
9.24. For the house sales data in Table 9.4, Table 9.12 shows a regression analysis relating selling price to number of bedrooms.(a) Report the prediction equation, and interpret the slope.(b) Using the sample slope and the standard deviations, find the correlation. Interpret its value.(c) Report r
9.23. For data on several nations, we want to describe whether percentage of people using the Internet is more strongly associated with per capita GDP or with the fertility rate.(a) Can we compare the slopes when GDP and fertility each predict Internet use in separate regression equations? Why or
9.22. In the UN Human Development Report, one variable measured was x = percentage of adults who use contraceptive methods. Table 9.11 shows part of a printout for a regression analysis using y = fertility (mean number of children per adult woman), for 22 nations listed in that report. For those
9.21. For 2004 GSS data, the correlation matrix for subject's education (EDUC), mother's education (MAEDUC), and father's education (PAEDUC) is EDUC PAEDUC MAEDUC EDUC 1.00 .40 .38 PAEDUC .40 1.00 .65 MAEDUC .38 .65 1.00 Interpret this matrix, identifying the pair of variables with the strongest
9.20. An article in the September 16, 2006 issue of The Economist showed a scattcrplot for many nations relatingy = annual oil consumption per person (in barrels) and x = GDP per person (in thousands of dollars). The (x,y) values shown on the plot were approximately (3, 1) India, (8, 2) China, (9,
9.17. For the study in Example 9.6 (page 267) of y = high school GPA and x = weekly number of hours viewing television, y = 3.44 — 0.03x.(a) The study reported that /--squared = 0.237.Interpret.(b) Report and interpret the correlation.(c) Suppose you found the correlation only for those students
9.15. A high school student analyzes whether a relationship exists between x = number of books read for pleasure in the previous year and y = daily average number of hours spent watching television.For her three best friends, Table 9.10 shows the observations.(a) Construct a scatterplot. From
9.14. Table 9.16 in Exercise 9.39 shows countywidc data for several variables in Florida. For those counties. Table 9.9 shows part of the printout for the regression analysisrelatingy = median income(thousand of dollars) to x = percent of residents with at least a high school education.(a) Report
9.13. A report summarizing the results of a study on the relationship between a verbal aptitude test x and a mathematics aptitude test y states that x - 480. y - 500,% - 80, Sy - 120, and r - 0.60.Using the formulas for the correlation and for the least squares estimates, find the prediction
9.12. For nations listed in the Human Development Report, the correlation with percent ofpeople using the Internet is 0.888 for per capita gross domestic product (GDP, a summary description of a nation's wealth), 0.818 for percent using cell phones, 0.669 for literacy rate, -0.551 for fertility
9.11. Figure 9.21 is a scatterplot relating y = percent of people using cell phones and x = per capita gross domestic product (GDP) for nations listed in the Human Development Report.(a) Give the approximate x- and _v-coordinatcsfor the nation that has the highest (i) cell-phone use, (ii) GDP.(b)
9.10. In the 2000 Presidential election in the U.S., the Democratic candidate was A1 Gore and the Republican candidate was George W. Bush.In Palm Beach County, Florida, initial election returns reported 3407 votes for the Reform party candidate, Pat Buchanan. Some political analysts thought that
9.9. For the data in Table 9.1 on y = violent crime rate and x = poverty rate, the prediction equation is y = 209.9 + 25.5x.(a) Interpret the y-intcrccpt and the slope.(b) Find the predicted violent crime rate and the residual for Massachusetts, which had x = 10.7 and y = 805. Interpret.(c) Two
9.8. A college admissions officer uses regression to approximate the relationship between y = college GPA and x = high school GPA (both measured on a four-point scale) for students at that college.(a) Which equation is more realistic: y =0.5 + 7.Ox, or y = 0.5 + 0.7x? Why?(b) Suppose the prediction
9.7. For recent UN data from 39 countries on y = per capita carbon dioxide emissions (metric tons per
9.6. A study5 of mail survey response rate patterns of the elderly found a prediction equation relatingx =age (between about 60 and 90) andy = percentage ofsubjects responding of y = 90.2 - 0.6x.(a) Interpret the slope.(b) Find the predicted response rate for a (i) 60-ycar-old, (ii) 90-ycar-old.
9.5. Look at Figure 2 in www.ajph.org/cgi/reprint/93/4/652?ck=nck, a scatterplot for U.S. states with correlation 0.53 between x = child poverty rate andy =child mortality rate. Approximate the y-intercept and slope of the prediction equation shown there.
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