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statistical sampling to auditing

Questions and Answers of Statistical Sampling To Auditing

12.18. Table 12.29 summarizes responses on political ideology in the 2014 General Social Survey by religion and sex. The P-value is Explain what this means in the context of this example, and
12.19. Table 12.30 shows results of an ANOVA on y =depression index by gender and marital status (married, never married, divorced). State the sample size and fill in the blanks in the ANOVA table.
12.20. Twenty-five students in a statistics class were surveyed about their attitudes toward divorce. Each received a response score according to how many from a list of seven possible reasons were
12.21. The prediction equation ˆy = 16+2s+3r+8(s×r)relates y = annual income (thousands of dollars), s = sex(s = 1 for men, s = 0 for women), and r = race (r = 1 for whites, r = 0 for blacks). By
12.22. For the 2014 GSS, Table 12.32 shows sample means of political ideology (higher values being more conservative), classified by gender and by race, for those over 50 in age. For H0: no
12.23. Refer to Table 12.15 (page 382) about the influence of three entertainment types on children.(a) Using software, conduct the repeated-measures analyses of Section 12.5.(b) Suppose you scored
12.24. Recently the General Social Survey asked respondents,“Compared with 10 years ago, would you say that American children today are (1) much better off, (2) better off, (3) about the same, (4)
12.25. The General Social Survey asks respondents to rate various groups using the “feeling thermometer” on a scale of 0 (most unfavorable) to 100 (most favorable).We plan to study how the mean
12.26. Using software, conduct the repeated-measures ANOVA of the anorexia data in Table 12.18 (page 385), available at the text website. Interpret results.
12.27. Refer to the Students data file (Exercise 1.11 on page 21), with response variable the number of weekly hours engaged in sports and other physical exercise. Using software, conduct an analysis
12.28. For y=number of times used public transportation in previous week and x = number of cars in family (which takes value 0, 1, or 2 for the given sample), explain the difference between
12.29. Goto the GSS website sda.berkeley.edu/GSS.(a) Analyze the change over time (GSS variable YEAR)in the mean of political ideology (POLVIEWS) by political party identification (PARTYID). Compare
12.30. A study5 described an experiment that randomly assigned participants to receive $3 to spend on themselves(self-interest), or to receive $3 to donate to a nonprofit charity (imposed charity),
12.31. A study6 compared verbal memory of men and women for abstract words and for concrete words. It found a gender main effect in favor of women. It also reported,“There was no sex × word-type
12.32. (a) Explain carefully the difference between a probability of Type I error of 0.05 for a single comparison of two means and a multiple comparison error rate of 0.05 for comparing all pairs of
12.33. For a two-way classification of means by factors A and B, at each level of B the means are equal for the levels of A. Does this imply that the overall means are equal at the various levels of
12.34. Table 7.29 (page 224) summarized a study that reported the mean number of dates in the past three months.For men, the mean was 9.7 for the more attractive and 9.9 for the less attractive. For
12.35. Construct a numerical example of means for a twoway classification under the following conditions:(a) Main effects are present only for the row variable.(b) Main effects are present for each
12.36. The 25 women faculty in the humanities division of a college have a mean salary of $76,000, and the five women in the science division have a mean salary of$90,000. The 20 men in the
12.37. Refer to Exercise 12.20. The students were also asked about their attitudes toward abortion. Each received a score according to how many from a list of eight possible reasons for abortion she
12.38. True or false? Suppose that for subjects aged under 55, there is little difference in mean annual medical expenses for smokers and nonsmokers, but for subjects aged over 55 there is a large
12.39. Analysis of variance and regression are similar in the sense that(a) They both assume a quantitative response variable.(b) They both have F tests for testing that the response variable is
12.41. For four means, a multiple comparison method provides 95% confidence intervals for the differences between the six pairs. Then(a) For each confidence interval, there is a 0.95 chance that it
12.42. Interaction terms are needed in a two-way ANOVA model when(a) Each pair of variables is associated.(b) Both explanatory variables have significant effects in the model without interaction
12.43. Use the ANOVA applet at www.pearsonglobal editions.com/Agresti to illustrate how betweengroups and within-groups variability affect the result of the ANOVA F test. Print results of two
12.44.* This exercise motivates the formula for the between-groups variance estimate in one-way ANOVA.Suppose the sample sizes all equal n and the population means all equal μ. The sampling
12.45.* You form a 95% confidence interval in five different situations, with independent samples.(a) Find the probability that (i) all five intervals contain the parameters they are designed to
13.1. The regression equation relating y = education(number of years completed) to race (z = 1 for whites, z = 0 for nonwhites) in a certain country isE(y) = 11+2z.The regression equation relating
13.2. Table 3.9 on page 65 showed data for several nations on y = C02 emissions (in metric tons per capita) and x =per capitaGDP(in thousands of dollars). Let z =whether the nation is in Europe (1 =
13.3. A regression analysis for the 100th Congress predicted the proportion of each representative’s votes on abortion issues that took the “pro-choice” position.6 The prediction equation
13.4. For 2014 data, the GSS website yields the prediction equation ˆy = 9.59+0.166x1+0.347x2 for y = highest year of school completed, x1 = sex (1 = male, 2 = female), and x2 = highest year of
13.5. Based on a national survey, Table 13.16 shows results of a prediction equation for y = alcohol consumption, measured as the number of alcoholic drinks the subject drank during the past
13.6. Consider the results in the previous exercise.(a) Marital status has three estimates. Dividing the coefficient of the divorced dummy variable by its standard error yields a t statistic. What
13.7. For the Houses data file at the text website, Table 13.17 shows results of modeling y = selling price (in dollars)in terms of size of home (in square feet) and whether the home is new (1 = yes;
13.8. For the previous exercise, Table 13.18 shows results of fitting the model allowing interaction.(a) Report the lines relating the predicted selling price to the size for homes that are (i) new,
13.9. Using software, replicate all the analyses shown in Sections 13.1 and 13.2 using the Income data file at the text website.
13.10. The software outputs in Table 13.19 show results of fitting two models to data from a study of the relationship between y = percentage of adults voting, percentage of adults registered to
13.11. Refer to the previous exercise. The means of percentage registered for the three categories are ¯x1 = 76.2,¯x2 = 49.5, and ¯x3 = 39.7. The overall mean ¯x = 60.4.(a) Find the adjusted mean
13.12. Table 13.1 did not report the observations for 10 Asian Americans. Their (x, y) values were Subject 1 2 3 4 5 6 7 8 9 10 Education 16 14 12 18 13 12 16 16 14 10 Income 70 42 24 56 32 38 58 82
13.13. Exercise 13.1 reported the regression equation relating y = education to race (z = 1 for whites) and to father’s education (x) of E(y) = 3 + 0.8x − 0.6z. The means ¯y = 11 for nonwhites,
13.14. Refer to the regression modeling of the familyclustered data in Table 13.13. Add to the Family data file the data for family 9, who had (y, x1, x2) values (0, 2, 0) and (1, 2, 1). Fit the
13.15. Refer to the Students data file (Exercise 1.11).Using software, prepare a report presenting graphical, descriptive, and inferential analyses with(a) y = political ideology and the predictors
13.16. Refer to the data file your class created in Exercise 1.12. For variables chosen by your instructor, use regression analysis as the basis of descriptive and inferential statistical analyses.
13.17. Refer to the OECD data file at the text website, shown in Table 3.13 (page 70). Pose a research question about how the human development index and whether a nation is in Europe relate to
13.18. An article7 on predicting attitudes toward homosexuality modeled a response variable with a four-point scale in which homosexual relations were scaled from 1 =always wrong to 4 = never wrong,
13.19. For the 2014 GSS, Table 13.20 shows estimates(with se values in parentheses) for four regression models for y = political party identification in the United States, scored from 1 = strong
13.20. Table 13.21 shows output for GSS data with y =index of attitudes toward premarital, extramarital, and homosexual sex, for which higher scores represent more permissive attitudes. The
13.21. You plan a study of factors associated with fertility(a woman’s number of children) in a Latin American city.Of particular interest is whether migrants fromother cities or migrants from
13.22. Analyze the Houses2 data file at the text website by modeling selling price in terms of size of house and whether it is new.(a) Fit the model allowing interaction, and test whether the
13.23. For the Crime2 data file at the text website, let z be a dummy variable for whether a state is in the South, with z = 1 for AL, AR, FL, GA, KY, LA, MD, MS, NC, OK, SC, TN, TX,VA, WV.(a) Not
13.24. You have two groups, and you want to compare their regressions of y on x, to test the hypothesis that the true slopes are identical for the two groups. Explain how to do this using regression
13.25. In analyzing GSS data relating y = frequency of having sex in the past year to frequency of going to bars, DeMaris (2004, p. 62) noted that the slope for unmarried subjects is more than double
13.26. Let y = death rate and x = mean age of residents, measured for each county in Louisiana and in Florida.Sketch a hypothetical scatterplot, identifying points for each state, when the mean death
13.27. Draw a scatterplot with sets of points representing two groups such that H0: equal means would be rejected in a one-wayANOVAbut not in an analysis of covariance.
13.28. For a regression model fitted to annual income(thousands of dollars) using predictors age and marital status, Table 13.23 shows the sample mean incomes and the adjusted means. How could the
13.29. In the model E(y) = α + β1x + β2z, where z = 1 for females and z = 0 formales,(a) The categorical factor has two categories.(b) One line has slope β1 and the other has slope β2.(c) β2 is
13.30. In the United States, the mean annual income for blacks (μ1) is smaller than for whites (μ2), the mean number of years of education is smaller for blacks than for whites, and annual income
13.31. Summarize the differences in purpose of a one-way analysis of variance and an analysis of covariance.
13.32.* Suppose we use a centered variable for the covariate and express the interaction model when the categorical factor has two categories as E(y) = α + β1(x − μx) + β2z + β3(x − μx) ×
13.33.* Using the graphical representation in Figure 13.10, explain why yi= yi+ b( ¯x − ¯xi), where b is the estimated slope. So, when b > 0, yi is adjusted upward if ¯x > ¯xi and adjusted
13.34. Explain the reason for entering random effects into a regression model. Describe a study in which it would be helpful to use this approach.
13.35. Explain what is meant by the term mixed model, and explain the distinction between a fixed effect and a random effect.
13.36. Summarize advantages of using a linear mixed model to analyze repeated-measures data, compared to using standard repeated-measures ANOVA.
13.37. A recent study8 examined the role of family structure in the financial support parents provide for their children’s college education. Using data for 5070 children from 1519 families from
14.1. For Example 11.2 (page 324) on y = mental impairment, x1 = life events, and x2 = SES, the multiple regression model has outputSES had a P-value of 0.011 in the bivariate model containing only
14.2. Table 11.23 (page 359) showed results of a multiple regression using nine predictors of the quality of life in a country.(a) In backward elimination with these nine predictors, can you predict
14.3. For the Houses2 data file at the text website, Table 14.9 shows a correlation matrix and a model fit using four predictors of selling price.With these four predictors,(a) For backward
14.4. Refer to the previous exercise. Using software with these four predictors, find the model that would be selected using the criterion. (a) R2 adj, (b) PRESS, (c) AIC.
14.5. Use software with the Crime2 data file at the text website, excluding the observation for D.C. Let y = murder rate. For the five explanatory variables in that data file(excluding violent crime
14.6. Figure 14.13 is a plot of the residuals versus the predicted y-values for the model discussed in Example 13.1 (page 402) relating income to education and racial–ethnic group.What does this
14.7. For the data for 21 nations in the UN2 data file at the text website that are not missing observations on literacy, Table 14.10 shows various diagnostics from fitting the multiple regression
14.8. For the Crime2 data file at the text website, fit the linear regression model with y = violent crime rate and x = percentage living in metropolitan areas, for all 51 observations.(a) Plot the
14.9. In Exercise 14.3, backward elimination and forward selection choose the model with explanatory variables SIZE, BATHS, and NEW.(a) Fit this model with the Houses2 data set. Inspect the leverages
14.10. For the Houses2 data file, fit the model to y = selling price using house size, whether the house is new, and their interaction.(a) Show that the interaction term is highly significant.(b)
14.11. Three variables have population correlationsρx1x2= 0.85, ρyx1= 0.65, and ρyx2= 0.65. For these, the partial correlations are ρyx1·x2= ρyx2·x1= 0.244. In a sample, rx1x2= 0.90, ryx1=
14.12. For a data set for 100 adults on y = height, x1 =length of left leg, and x2 = length of right leg, the model E(y) = α + β1x1 + β2x2 is fitted. Neither H0: β1 = 0 nor H0: β2 = 0 has a
14.13. Refer to the plot of residuals in Figure 14.13 for Exercise 14.6.(a) Explain why a more valid fit may result from assuming that income has a gamma distribution, rather than a normal
14.14. Refer to the data from Example 14.7 on fertility rates and GDP (page 453). To allow for greater variation at higher values of mean fertility, fit a quadraticGLMwith a gamma distribution for
14.15. Table 14.12 shows the results of fitting two models to 54 observations on y = mental health score, x1 = degree of social interaction, and x2 = SES. The variables x1 and x2 are measured on
14.16. Sketch the following mathematical functions on the same set of axes, for values of x between 0 and 4. Use these curves to describe how the coefficients of x and x2 affect their shape.(a) ˆy =
14.17. For the Houses data file, Table 14.13 shows results of fitting a quadratic regression model with s = size as the predictor.(a) Interpret the coefficients of this equation.What shape does it
14.18. Refer to the previous exercise.(a) Using size as a straight-line predictor, r2 = 0.695, whereas R2 = 0.704 for the quadratic model. Is the degree of nonlinearity major, or minor? Is the linear
14.19. The Crime2 data file at the text website illustrates how a single observation can be highly influential in determining whether the model should allow nonlinearity.(a) With all 51 observations,
14.20. For data from 2005 to 2011 from Facebook on y =number of people (in millions) worldwide using Facebook, the prediction equation ˆy = 2.13(2.72)x fits well, where x = number of years since
14.21. For data shown in the article “Wikipedia: Modelling Wikipedia’s growth” at en.wikipedia.org, the number of English language articles inWikipedia was well approximated from 2001 to 2008
14.22. For United Nations data on y = world population size (billions) between 1900 and 2010, the exponential regression model with x = number of years since 1900 givesˆy = 1.4193(1.014)x.(a)
14.23. Draw rough sketches of the following mathematical functions on the same set of axes, for x between 0 and 35.(a) ˆy = 6(1.02)x. (ˆy = predicted world population size in billions x years after
14.24. Consider the formula ˆy = 4(2)x.(a) Plot ˆy for integer x between 0 and 5.(b) Plot loge ˆy against x. Report the intercept and slope of this line.
14.25. For white men in the United States, Table 14.14 presents the number of deaths per thousand individuals of a fixed age within a period of a year.TABLE 14.14 Age Death Rate (Per Thousand)30 3 40
14.26. Consider the fertility and GDP data in Table 14.6, from the FertilityGDP data file.(a) Using GLM software, fit the exponential regression model, assuming fertility rate has a (i) normal, (ii)
14.27. Refer to the Students data file (Exercise 1.11).(a) Conduct and interpret a regression analysis using y =political ideology, selecting predictors from the variables in that file. Prepare a
14.28. Refer to the data file the class created in Exercise 1.12. Select a response variable, pose a research question, and build a model using other variables in the data set.Interpret and summarize
14.29. Analyze the Crime data set at the text website, deleting the observation for D.C., with y = violent crime rate. Use methods of this chapter. Prepare a report describing the analyses and
14.30. For the Mental data file at the text website and the model predicting mental impairment using life events and SES, conduct an analysis of residuals and influence diagnostics.TABLE 14.15 Year
14.31. Table 14.15 shows the population size of Florida, by decade from 1830 to 2010. Analyze these data, which are the data file FloridaPop at the text website. Explain why a linear model is
14.32. For the UN2 data file at the text website, using methods of this chapter,(a) Find a good model relating x = per capita GDP to y =life expectancy. (Hint: What does a plot of the data
14.33. Give an example of a response variable and a pair of explanatory variables for which an automated variable selection procedure would probably produce a model with only one explanatory
14.34. A sociologist’s first reaction upon studying automated variable selection routines was that they had the danger of leading to “crass empiricism” in theory building.From a theoretical
14.35. Give an example of two variables that you expect to have a nonlinear relationship. Describe the pattern you expect for the relationship. Explain how to model that pattern.
14.36.You plan to model y = fertility rate (the mean number of children per adult woman) and x = per capita gross domestic product (GDP, in tens of thousands of dollars). For the ordinary bivariate

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