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statistical sampling to auditing

Questions and Answers of Statistical Sampling To Auditing

14.37. Using the formula s/s j(n − 1)(1 − R2j) for the standard error of the estimator of βj in multiple regression, explain how precision of estimation is affected by(a) Multicollinearity.(b)
14.38. A recent newspaper article quoted a planner in a city as saying, “This city has been growing at the rate of 3.2% per year. That is not slow growth by any means. It corresponds to 32% growth
14.39. Example 14.8 showed a predicted U.S. population size (in millions) x decades after 1890 of ˆy =73.175(1.130)x.(a) Show this is equivalent to 1.23% predicted growth per year. [Hint: (1.0123)10
14.40. You invest $1000 in an account with interest compounded annually at 9%.(a) How much money do you have after x years?(b) How long does it take your savings to triple in size?For multiple-choice
14.41. In the model E(y) = α + β1x + β2x2, the coefficientβ2(a) Is the mean change in y as x2 is increased one unit with x held constant.(b) Is a curvature coefficient that describes whether the
14.42. The log transformation of the mean response in regression is useful when(a) E(y) is approximately a logarithmic function of x.(b) E(y) is approximately an exponential function of x.(c) logE(y)
14.43. Forward selection and stepwise regression are similar in the sense that, if they have the same α-level for testing a term,(a) They always select the same final regression model.(b) They
14.44. Evidence of multicollinearity exists in a multiple regression fit when(a) Strong intercorrelations occur among explanatory variables.(b) The R2-value is very large.(c) The F test of H0: β1 =
14.45. True or false?(a) Adjusted R2 can possibly decrease when an explanatory variable is added to a regression model.(b) Possible effects of an influential observation include changing a
14.46. Select the best response for each of the following terms (not every response is used):Heteroscedasticity Multicollinearity Forward selection Interaction Exponential model Stepwise regression
14.47.* Show that using a cross-product term to model interaction assumes that the slope of the relationship between y and x1 changes linearly as x2 changes. How would you suggest modeling
14.48.* Forward selection is used with 10 potential explanatory variables for y. In reality, none are truly correlated with y or with each other. For a random sample, show that the probability equals
15.1. A logistic regression model describes how the probability of voting for Candidate X in an election depends on x = voter’s total family income (in thousands of dollars)in the previous year.
15.2. Refer to the previous exercise. When the explanatory variables are x1 = family income, x2 = number of years of education, and s = sex (1 = male, 0 = female), the prediction equation is
15.3. A sample of 54 elderly men take a psychiatric examination to determine whether symptoms of senility are present. A subtest of the Wechsler Adult Intelligence Scale (WAIS) is the explanatory
15.4. Table 15.19, the data file Credit at the text website, shows data for a sample of 100 adults randomly selected for an Italian study on the relation between annual income and having a travel
15.5. For first-degree murder convictions6 in East Baton Rouge Parish, Louisiana, between 1990 and 2008, the death penalty was given in 3 out of 25 cases in which a white killed a white, in 0 out of
15.6. Table 12.1 in Chapter 12 reported GSS data on political ideology (scaled 1 to 7, with 1 being most liberal) by party affiliation of 1 2 3 4 5 6 7 Democrat 5 18 19 25 7 7 2 Republican 1 3 1 11
15.7. A multination study of whether a country transitioned from autocracy to democracy during the study period7 reported the prediction equation logit[ˆP(y = 1)] = −3.30 + 0.55t +
15.8. Let P(y = 1) denote the probability that a randomly selected respondent supports current laws legalizing abortion, estimated using sex of respondent (s = 0, male; s = 1, female), religious
15.9. Table 15.21 summarizes logistic regression results from a study8 of how family transitions relate to first home purchase by young married households. The response variable is whether the
15.10. For Table 15.12 on page 493, Table 15.22 shows output for a logistic model treating marijuana use as the response variable and alcohol use and cigarette use as explanatory variables.(a) Set up
15.11. A sample of inmates being admitted to the Rhode Island Department of Corrections were asked whether they ever injected drugs and were tested for hepatitis C virus (HCV). The numbers who
15.12. Table 15.23 refers to individuals who applied for admission into graduate school at the University of California in Berkeley. Data10 are presented for five of the six largest graduate
15.13. Consider Table 8.16 on page 245, treating happiness as the response variable. Table 15.24 shows results of fitting the cumulative logit model logit[P(y ≤ j)] =αj + βx, using scores (1, 2,
15.14. Using software with Table 8.16, replicate the results shown in the previous exercise for the cumulative logit model. Indicate whether the sign for ˆβ agrees with the negative sign for ˆβ
15.15. Table 15.25 refers to passengers in autos and light trucks involved in accidents in the state of Maine. The table, available as the Accidents data file at the text website, classifies subjects
15.16. Explain why the cumulative logit model is not valid with a nominal response variable, but a baseline-category logit model is valid with an ordinal response variable.
15.17. A baseline-category logit model fit predicting preference for U.S. President (Democrat, Republican, Independent)using x = annual income (in $10,000) is log(πˆD/πˆ I) = 3.3 − 0.2x and
15.18. For a sample of people in a developed city, for the most recent time each person shopped for clothes, you plan to model the choice to shop downtown or on the Internet. Explanatory variables
15.19. Refer to the 3×7 table in Table 12.1 (page 364) on party identification and political ideology.(a) Fit a baseline-category logit model, treating party affiliation as the response and
15.20. Using software, replicate the results in Example 15.6 (page 490) on belief in an afterlife, sex, and race.
15.21. Consider the fit of the loglinear model (AC, AM,CM) to Table 15.12 for the survey of high school seniors.(a) Use the estimated expected frequencies in Table 15.14 to estimate the conditional
15.22. Refer to the loglinear model analyses reported in Examples 15.7 and 15.8 for use of marijuana, alcohol, and cigarettes. Use software to replicate all the analyses shown there.
15.23. For a four-way cross-classification of variablesw, x, y, and z, state the symbol for the loglinear model in which(a) All pairs of variables are independent.(b) x and y are associated, but
15.24. For Table 15.3 on the death penalty, the logistic model that has an effect of victims’ race but assumes that the death penalty is independent of defendant’s race(given victims’ race) has
15.25. Refer to the survey data for high school seniors in Table 15.12 and the goodness-of-fit statistics reported in Table 15.18 (page 499). Use these results to illustrate (a)when a model fits well
15.26. Refer to the Students data file (Exercise 1.11).Using software, conduct and interpret a logistic regression analysis using y = opinion about abortion with explanatory variables(a) Political
15.27. In a one-page report, analyze Table 15.7 by treating party affiliation as the response variable and political ideology as a quantitative explanatory variable. Fit an appropriate model, conduct
15.28. The data shown in Exercise 10.14 in Chapter 10 came from an early study on the death penalty and racial characteristics. Analyze those data using methods of this chapter. Summarize your main
15.29. One year, the Metropolitan Police in London, England, reported11 30,475 people as missing in the year ending March 1993. For those of age 13 or less, 33 of 3271 missing males and 38 of 2486
15.30. In a study of whether an educational program makes sexually active adolescents more likely to obtain condoms, adolescents were randomly assigned to two experimental groups. The educational
15.31. A Canadian survey of factors associated with whether a person is a hunter of wildlife showed the results in Table 15.27. Explain how to interpret the results in this table. The study
15.32. Astudy13 compared the relative frequency of mental health problems of various types among U.S. Army members before deployment to Iraq,U.S. Army members after serving in Iraq, U.S. Army members
15.33. A report (www.oas.samhsa.gov) by the Office of Applied Studies for the Substance Abuse and Mental Health ServicesAdministration about factors that predict marijuana use stated, “Multiple
15.34. Analyze the data in Exercise 8.16 (page 253) on happiness and marital status using a cumulative logit model. Interpret the results in a report of about 200 words.
15.35. For Table 15.4 (page 479), show that the association between the defendant’s race and the death penalty verdict satisfies Simpson’s paradox.What causes this?
15.36. For a person, let y = 1 represent death during the next year and y = 0 represent survival. For adults in the United Kingdon and in the United States, the probability of death is well
15.37. State the symbols for the loglinear models for categorical variables that are implied by the causal diagrams in Figure 15.5. TABLE 15.27 Coef. S.E. Wald Sig Exp(B) Constant -5.04 0.16 943.1
15.38.* For the logistic regression model, from the linear approximation β/4 for the rate of change in the probability at the x-value for which P(y = 1) = 0.50, show that 1/|β| is the approximate
15.39.* For a two-way contingency table, let ri denote the ith row total, let cj denote the jth column total, and let n denote the total sample size. Section 8.2 (page 230) stated that the cell in
15.40.* Logistic regression has infinite maximum likelihood estimates when the cases with y = 1 are separate from the cases with y = 0 in the space of explanatory variable values.When this happens,
15.41.* Explain what is meant by the absence of statistical interaction in modeling the relationship between a response variable y and two explanatory variables x1 and x2 in each of the following
1. In Table 9.16 in Problem 9.24 regarding Flonda counties, refer to the vanables Y = crime rate (number per 1000 residents). X) = median income (thousands of dollars), and X2 = percent in urban
2. For students at Walden University, the relationship between college GPA (with range 040) and X1 high school GPA (range 0-4.0) and X2 = college board score (range 200-800) satisfies E(Y) =
3 Refer to the data in Table 9.13 in Problem 9.17, Let Y = crude burth rate, X = women's economic activity, and X2 = GNP. The least squares equation is = 34.5313X- .64X2.a) Interpret the estimated
4 Refer to Example 11 1. Using computer software for the data in Problem 9.24 for those three variablesa) Construct box plots for cach variable and scatter diagrams and partial regression plots
5 Table 11 11 show's a SAS printout from fitting the multiple regression model to the data hom Table 9.1. excluding D.C., on Y = violent crime rate. X = poverty rate. and X2 = pescent living in
6. Repeat the previous exercise using software to fit the model with murder rate in Table 9.1 as the response variable.
7 Refer to Problem 11.5. With X3 = percentage of single-parent families also in the model. Table 11.12 shows results.a) Report the prediction equation and interpret the coefficientsb) Report R, and
8. Table 11.13 is part of a SPSS printout for fitting a regression model to the relationship between Y = number of children in family. X = mother's educational level (MEDUC) in years, and X2 father's
9 Refer to Problem 9.30 on feelings toward liberals, political ideology, and religious atten- dance. The sample size is small, but for illustrative purposes Table 11.14 shows results of fitting the
1 Studies of the degree of residential segregation between blacks and whites use the segre. gation index, defined as the percentage of nonwhites who would have to change the block on which they live
2. Refer to the previous exercise.a) State the assumptions for the analysis, and show that at least two of them may be vio- lated. What is the impact?b) Construct the regression model with dummy
3. A consumer protection group compares three different types of front bumpers for a bi and of automobile A test is conducted by driving an automobile into a brick wall at 15 mules per hour. The
4. Table 1227 show's scores on the first quiz (maximum score 10 points) in a beginning French course. Students in the course are grouped as follows: Group A. Never studied foreign language before,
5. The General Social Survey asks respondents to rate various groups using the "feeling ther- mometer Ratings between 50 and 100 mean you feel favorable and warm toward the group, whereas ratings
6. Refer to Table 12.19.a) Using software, conduct a one-way ANOVA for the 72 observations at time = after. Verify that the F test statistic companng the three treatments at that time equals 8 65,
7. Table 12 29 is a contingency table summarizing responses on political ideology in the 1991 General Social Survey by race and gender. Table 12.30 shows results of using SAS software to conduct an
8. Refer to the previous exercise, using the black sample onlya) Conduct an ANOVA comparing the two groups. Interpret.b) How does your analysis relate to the methods of Chapter 7 for comparing
9 Use software with the data in Table 9.4a) Conduct au ANOVA to test equality of the mean selling prices for homes with one. Two, and three bathrooms. Interpret.b) Explain the difference between
10. Refer to Table 9.4 In that data set, whether a house is new is a dummy variable Using software, put this as the sole predictor of selling price in a regression analysis.a) Conduct the test for
11. A psychologist compares the mean amount of time of REM sleep for subjects under three conditions. She uses three groups of subjects, with four subjects in each group. Table 12.31 shows a SAS
12. For g groups with large sample sizes, we plan to compare sinultaneously all pairs of popu- lation means. We want the probability to equal at least 80 that the entire set of confidence intervals
13. A geographer compares residential lot sizes in four quadrants of a city To do this, he randomly samples 300 records from a city file on home residences and records the lot sizes (in thousands of
14. A study compares the inean level of contributions to political campaigns in Pennsylvania by registered Democrats, registered Republicans, and unaffiliated votersa) Write a regression equation for
15. Use computer software to reproduce the one-way ANOVA results reported in Table 12.2 for Example 12 1.
16. According to the US Department of Labor, the mean hourly wage in 1994 was $15.71 for a college graduate and $9.92 for a high school graduate. In 1979, the means (in 1994 dollars) were $15.52 for
17. Refer to Table 7.18 in Problem 7.40, which summanzes the mean number of dates in the past three months by gender and hy level of physical atu activeness. Do these data appear to show interaction?
18 A recent regression analysis of college faculty salaries in 1984 (M. Bellas, American So ciological Review. Vol. 59, 1994, p. 807) included a large number of predictors, including a dummy variable
19. Refer to the prediction equation = 4 58.71P-54P-08G for the no interaction model in Example 12.5.a) Using it. find the estimated means for each of the six cells, and show that they satisfy a lack
20 Use software with Table 12.11, analyzed in Section 12.5.a) Fit the no interaction model, and verify the results given there.b) Fit the interaction model. Compare SSE for this model to SSE for the
21. Consider the regression model E(Y) = a + BG + BR+B(GR), where Y = income (thousands of dollars), G= gender (G=1 for men and G = 0 for women), and R = race (R=1 for whites and R == 0 for
22. Refer to Problem 12.7. Table 12.33 shows the result of using SAS to conduct a two-way ANOVA, with both gender and race as predictors. The first panel of the table shows the result of the model
23. Table 12 34 shows results of an ANOVA on Y = depression index and the predictors gen- der and marital status (married, never married. divorced).a) State the regression model for this analysis.b)
24. The 25 women faculty in the humanities division of a college have a mean salary of $46,000, whereas the five in the science division have a mean salary of $60,000. On the TABLE 12.34 Suni of
25 Refer to Example 12.6 and Table 12.16.a) Using software, conduct the repeated measures analyses of Section 12.6b) Suppose one scored the influence categones (1,2. 3. 4. 5). Would this have any
26. Recently the General Social Survey asked respondents. "Compared with ten years ago. would you say that American children today arc (1) much better off, (2) better off, (3) about the same. (4)
27 Refer to the previous exercise. The first five respondents were female, and the last five were male. Analyze these data using both gender and issue as factors.a) Identify the between-subjects and
28. Refer to Problem 125 When these subjects were asked to rate conservatives. the mean responses were 61.9 during 1983-87 and 60.7 during 1988-91. Explain why a two-way ANOVA using time (1983-87.
29. Upjohn, a pharmaceutical company, conducted a randomized clinical tnal comparing an active hypnotic drug with a placebo for patients suffering from insomnia. The outcome is patient response to
30 Table 12.37 shows results of irsing SPSS in Example 12.7 with Table 12 19a) Explain how to use the information in this table to conduct the test of no interaction between treatment and time.b)
31. Using software, conduct the repeated measures ANOVA in Example 12.7 with Table 12.19. Concepts and Applications
32. Refer to the WWW data sei (Problem 1.7). with response variable the number of weekly hours engaged in sports and other physical exercise. Using software, conduct an analysis of variance and
33 Refer to the data file created in Problems 1.7 For variables chosen by your instructor. use ANOVA methods and related inferential statistical analyses. Interpret and summarize your findings.
34. The General Social Survey has frequently asked respondents how they would rate van- ous countries on a scale from -5 to +5, where -5 indicates the country is disliked very much and +5 indicates
35. A random sample of 26 female students at a major university were surveyed about their attitudes toward abortion. Each received a score on abortion attitude according to how many from a list of
36. Table 12.40, based on data from the 1989 General Social Survey, is a contingency table summarizing responses of 29 subjects regarding government spending on the environ-ment, assistance to big
37. Refer to the WWW data set in Problem 1.7. Use repeated measures analyses to model the weekly number of hours of recreation in terms of type of activity (levels S = sports and physical exercise, T
38. An experiment used four randomly selected groups of five individuals each. The overall sample mean was 60.a) What did the data look like if the one-way ANOVA for comparing the means had test

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