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statistical sampling to auditing

Statistical Methods For The Social Sciences 3rd Edition Alan Agresti, Barbara Finlay - Solutions

60. The P-value for testing H = 100 against H. 100 is P = .001. This indicates thata) There is strong evidence that = 100b) There is strong evidence that 100.c) There is strong evidence that u > 100d) There is strong evidence that u < 100e) If u were equal to 100 it would be unusual to obtain data
61. Refer to the previous problem. Suppose the value of the test statistic was = 329 Thena) There is strong evidence that u = 100.b) There is strong evidence thatc) There is strong evidence that > 100.
62. Refer to Problem 6.30. When we inake a decision using = .05. this ineans thata) If the plant is not exceeding the limit, but actually = 500. there is only a 5% chance that we will conclude that they are exceeding the limit.b) If the plant is exceeding the limit. there is only a 5% chance that
63 True or False P(Type II error) = 1-P(Type I error). Explain.
64. True or False. If we reject Ha using or = .01, then we also reject it using u = .05. Explain.
65. An article in an anthropology journal reports P = .043 for testing Ho. = 0 against He0. True or False If the authors had instead reported a 95% confidence interval for . then the interval would have contained zero. Explain, and discuss what one could learn from the confidence interval but not
66.a) Define (i) P-valuc. (ii) a-level. (iii) Type ll error, (iv) rejection region. (v) power.b) Explain the difference between one-sided and two-sided bypotheses. and explain how this affects calculation of the P-value
67. Explain why the terminology "do not reject Ha" is preferable to "accept Ho."
68 A randoin sample of size 40 has = 120 The P-value for testing Ho = 100 against H, 100 is P = .057 Explain what is inconect about each of the following inter- pretations of this P-value, and provide a proper interpretation.a) The probability that the null hypothesis is correct equals .057.b) The
69. *The P-value for testing H. 100 against H. >100 is P = 043 Does a 95% confidence interval for contain 100? Explain.
70 Explain why one can interpret the P-value as the sanallest a-level at which one can reject Hn, that is, P equals the sinallest level at which the data are significant. Illustrate using the P-value of 057 from Problem 6 68
71. Refer to Example 6.2 and to the correspondence between results of confidence intervals and two-sided tests Since P = 52 in that example, and since 1.52 = 48, explain why the 48% confidence interval is the narrowest confidence interval centered about 1" that contains 404.0
72. + We know the sample incan Y of a measurements. Show that if we know (n - 1) of those measurements, then we can determine the remaining observation. In other words. given the value of . the values of (1) observations determine the remaining one. In sunnanzing scores on a quantitative variable,
73. 'A researcher conducts a significance test every time she analyzes a new data set. Over time, she conducts 100 testsa) Suppose the null hypothesis is uue in every case. What is the distribution of the number of times she rejects the null hypothesis at the 05 level?b) Suppose she rejects the
74. * Each year in Liverpool. New York, a public librarian estimates die mean number of times the books in that library have been checked out in the previous year. To do this, the librarian randomly samples computer records for 100 books and forms a 95% confidence interval for the mean This has
75. * Refer to Problem 6.53. The process was recently modified because the outcoine 0 tended to occur too frequently. Using these data, test whether the proportion of times that would occur in the long run equals .1, the value expected for a proper random number generator, versus the alternative
76. *Refer to Problem 6.37a) For what values of the number of wins X can you reject Ho = .50 in favor of H.50. using a = .05?b) For what values of X can you reject Ho using a = 01? (Note: For small samples with discrete data, it may not be possible to achieve very small P-values.)c) * Suppose you
77. Let denote the probability of Type II error. For an o = .05-level test of Ho: p=0 against Hu> based on n = 30 observations = 36 at =4. Select the correct response(s).a) At = 5, 8 > .36.b) If a01, then at A = 4, B>.36.c) If = 50, then al = 4. > .36.d) The power of the test is .64 at = 4.e) This
1. In the 1982 General Social Survey. 350 subjects reported the time spent every day watch- ing television. The sample mean was 4 1 hours, with standard deviation 3.3. In the 1994 General Social Survey, 1965 subjects reported a mean time spent watching television of 2.8 hours, with standard
2 Refer to Table 6.2 and Example 6 7. Table 7.9 is a computer printout that summarizes the responses on the seven-point poliucal ideology scale for the surveys in 1978 and in 1994.a) Are these samples independent or dependent?b) Construct a 95% confidence interval for the difference between the
3. Refer to Problem 5.39 and Table 54. Construct a 99% confidence interval for the dif- ference between the mean number of hours employed per week for men and for women. Interpret Based on this interval, indicate what result would occur in a two-sample test comparing the means. Explain.
4. A recent study compared substance use, delinquency psychological well-being, and so- cial support anong various family types. lor a sample of urban Aincan-American ado- lescent males (M. Zimmerman et al., Child Development. Vol 66. 1995. pp. 1598-1613). The sample contained 108 subjects from
5. Refer to the preceding exercise. The youths also responded to a battery of questions that provides a measure of perceived parental support. This measure had sample means of 46 (s=9) for the single-mother households and 42 (s = 10) for the households with both bio-logical parents. Consider the
6. For 30 female assistant professors selected at random from arts and science departments in a large state university system, the mean academic year salary is $41,000 The mean salary for a random sample of 50 male assistant professors is $41.800. The sample stand- ard deviations are $3000 for
7. Seegmiller et al. (J. Psychology, Vol. 102, 1979, pp. 215-224) studied the effect of tester sex on sex-role differentiation scores of a sample of preschool children. For the Occupa- tional Preference Test, children were asked to give three choices of what they wanted to be when they grew up.
8. Families headed by low-wage workers may be more likely to be living in poverty now than two decades ago. According to a report by the Center on Budget and Policy Priorities, in 1977 7,7% of families with children in which the head of the household worked were below the poverty level: in 1993.
9. Chatterjee et al (1995. p 132) described two studies about the effect of condoms in reduc- ing the spread of AIDS. One two-year Italian study followed heterosexual couples where one partner was infected with the HIV virus. Of 171 couples who always used condoms, 3 partners became infected with
10 For a random sample of 1600 Canadians taken in January, 880 people indicate approval of the prime minister's performance. A similar poll a month later of a separate random sample of 1600 Canadians has a favorable rating by 944 people. Let x, denote the true proportion in January that approve of
11. The National Health Interview Survey conducted of 42.000 adults by the U.S. National Center for Health Statistics in 1991 indicated that 25.6% of adults were current smokers A similar study conducted in 1965 indicated that 42.4% were cunent smokersa) Construct a 95% confidence interval for the
12 Refer to Example 7.3.a) Find point estimates of the proportions of Americans who disagree with the statement about women's roles in 1982 and in 1994.b) Find a 95% confidence interval for the change in the disagree proportion, and compare it to the interval found following Example 7.3 for the
13. The General Social Survey asks, "Do you favor or oppose the death penalty for persons convicted of murder?" In 1982, 154 were in favor and 165 opposed In 1994. 2215 were in favor and 580 were opposed. Construct a 95% confidence interval for the difference between the proportions in favor of the
14. In a survey conducted in 1992 by the Wight State University School of Medicine. senior high school students were asked if they had ever used naijuana. Of the females sam- pled. 445 said yes and 675 said no: of the males sampled. 515 said yes and 641 said no. Compare and interpret these
15 A study using a probability sample from the 1984 National Health Interview Study (R. Coward et al., The Gerontologist. Vol. 35, 1995. pp. 24-34) reported that the percent of respondents with income below the poverty level was 11.3% for residents of metropolitan areas (n=7331) and 20.6% for
16 Table 7.10 shows results from a recent General Social Survey on two variables. gender and whether one believes in an afterlife.a) Which of the two variables is more naturally treated as the response variable?b) Let 7, denote the population proportion of females who would respond "yes" to wheth-
17. The 1974-1975 General Social Survey asked "Do you believe that women should take care of inning their homes and leave running the country up to men" For 1305 male re- spondents. 465 replied yes and 840 replicd no For 1566 feinale respondents. 555 replied yes and 1.011 replied no.a) Find a 95%
18. Newsweek magazine (September 19. 1983) reported results of a poll to investigate wheth- er there was a difference between the percentage of women and the percentage of men who approved of the way Ronald Reagan was handling his job as president Of 511 women interviewed, 40% indicated approval.
19. A study of bulimia among college women (J. Kern and T. Hastings, Journal of Clini- cal Psychology, Vol. 51, 1995. p. 499) considered the effect of childhood sexual abuse on vanous components of a Fanuly Environment Scale. For a measure of family cole- sion. the sample mean for the bulimic
20 The property values for three homes selected at random in the Forest Ridge subdivision are (in thousands of dollars) 110. 120. 130 The property values for two homes selected at random in the Hennitage subdivision arc 180, 200.a) Use small-sample methods to construct a 90% confidence interval for
21. For the WWW data for University of Florida social science students, described in Problem 1.7, the responses on political ideology had a mean of 3 18 and standard deviation of 1.72 for the 51 nonvegetarian students and a mean of 2.22 and standard deviation of .67 for the 9 vegetarian students.a)
22. Three editors of large-city newspapers are selected at random and asked to rate on a score of 0-100 the faimess of the news media in political reporting (0 corresponds to very un- fair). The same question is posed to three editors of small-town papers. The large-city editors gave scores of 55.
23 Refer to Example 7.5. The young adults were also asked whether they had ever had a same-gender sexual relationship. Table 7.12 shows results. Use software to test whether the probability of this is higher for those raised by lesbian mothers. Interpret. TABLE 7.12 Same-Gender Relationship Mother
24. Refer to the previous problem. Subjects were also asked whether they had ever had a same-gender sexual attraction. Table 7.13 shows a computer printout with results of the analysis. Interpret. TABLE 7.13 MOTHER Frequency ATTRACT No. Yes Total Heterosx 16 4 | 20 Lesbian 16 91 25 Statistic
25. Refer 10 Problcin 6.12. Compare the proportions of blacks and whites who think that af- firmative action has been good for the countrya) Using a 95% confidence interval Juterpretb) Using a significance test. Report the P-value, and interpret
26. Refer to Examples 74 and 76. Construct and interpre: a 90% confidence interval fora) In the independent samples caseb) In the dependent samples case.c) Compare results of the two analyses.
27. A recent study compared personality characteristics between 49 adult children of alco- holics and a control group matched on age and gender (D. Baker and L. Stephenson. Jour nal of Clinical Psychology, Vol 51. 1995. p. 694). On a measure of well-being, the 49 children of alcoholics had a mean
28. Refer to the previous problem. 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 They reported a t-score of 2.67 for the test comparing the means. As- suming that this is the result
29. Refer to Problem 6.26. The changes in heart rate for 15 males had a mean of -1.22 with standard deviation 19.7. Show how to compare the inean changes for females and males.a) using a 95% confidence interval,b) using a significance test Interpret in each case.
30. Each of a random sample of ten college freshmen takes a mathematics aptitude test both before and after undergoing an intensive training course designed to improve such test scores Then, the scores for each student are paired, as shown in Table 7.14. TABLE 7.14 Student Before After 1 60 70 2 73
31. A paired-difference experiment dealing with response latencies for noise detection under two conditions used a sample of twelve 9-month-old children and reported a sample incan difference of 70.1 and standard deviation of 49.4 for the differences (I Morgan and J. Saffran. Child Development, Vol
32. Refer to Example 7.7. Table 7.15 shows opinions about spending on the environment and on citics.a) Find the sample proportion favoring increased spending, for each itemb) Test whether the population proportions are equal. Report the P-value, and interpret.c) Construct a 95% confidence interval
33. Table 7 16 refers to a sample of juveniles convicted of a felony in Florida in 1987. Matched pairs were formed using criteria such as age and the number of prior offenses For each pair, one subject was handled in the juvenile court and the other was transferred to the adult court The response
34. A recent study used data from the Longitudinal Study of Aging to investigate how older people's health and social characteristics influence how far they live from their children (M. Silverstein, Demography. Vol 32, 1995. p. 35) Consider Table 7.17, which show's whether an older subject lives
35 Refer to the WWW data set (Problem 1.7). Using software. use a confidence interval and a test to compare males and females in terms ofa) The mean number of umes reading a newspaper. Interpretb) Opinions about legalized abortion. Interpret.
36. For the WWW data set (Problem 1.7), comparc Democrat and Republican students in terms of political ideology.a) Using back-to-back stem and leaf plots.b) Using numencal summariesc) Using inferential statistical methods. Interpret
37. For the 60 students in the WWW data set (Problem 17), compare the mean weekly time spent watching TV to the mean weekly tinie in sports and other physical exercise. using both descriptive and inferential methods.
38 Refer to the data file created in Problem 1.7. For vanables chosen by your instructor, con- duct inferential statistical analyses, using methods of this chapter. Prepare a report that summanzes and interprets your findings In this report. also use graphical and numeri- cal methods presented
39. Two new drugs have been proposed for treating subjects who suffer from high blood pres- sure. A sample of ten such subjects were randomly allocated to two groups for an ex- periment comparing the drugs. The five subjects in one group took drug A, and the five subjects in the other group took
40. The results in Table 7.18 are from a recent study of physical attractiveness and subjective well-being (E Diener et al.. Journal of Personality and Social Psychology, Vol 69, 1995. pp. 120-129). As part of the study, a sample of college students were rated by a panel on their physical
41. A study of the effects of race on professional football players' compensation (L Kaln, Industrial & Labor Relations Review, Vol. 45, 1992. p. 295) reported mean salanes, in thousands of dollars, in the National Football League in 1989 of 328 for 544 whites (s = 277) and 315 for 819 blacks (s =
42. For a sample of high school students in South Carolina, the percentage who reported they had had sexual intercourse was 65% for white males (n = 1147), 54% for white females (n=1314), 89% for black males (n = 612), and 71% for black females (n = 820) (D.Richter et al., Journal of School Health.
43. Refer to Problem 7.1. In 1982, 11 of the 350 subjects reported watching no television. In 1994. 74 of the 1965 subjects reported watching no television Analyze these data, and interpret
44. According to Newsweek magazine (July 31. 1995), the mean household income in 1994 was $40.708 for whites and $25,409 for blacks The article did not provide sample sizes oi standard deviations. Suppose it had reported a standard error of $200 for the mean for whites and $300 for the mean for
45. In the United States, the estimated annual probability that a woman over the age of 35 dies of lung cancer equals 00130 for current smokers and .00012 for nonsmokers (M. Pagano and K Gauvreau, Principles of Biostatistics, Belmont, CA: Duxbury Press. 1993. p. 134).a) Calculate and interpret the
46 Refer to the previous exercise. According to the US National Center for Health Statis- tics. in 1991 the probability that a male between the ages of 20 and 24 was a boinicide victim was .00164 for blacks and 00015 for whites. Compare these rates using the Jif- ference of proportions and the
47. A poll by Louis Harris and Associates of 1249 Americans in July 1994 indicated that 36% believe in ghosts and 37% believe in astrology.a) Is it valid to compare the proportions using inferential methods for independent sam- ples? Explain.b) Do you have enough information to compare them using
48. Table 7.19 compares two hospitals on the outcomes of patient admissions for severe pneu- monia. 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 categones. The
49. A recent General Social Survey asked respondents whether premarital sex was always wrong. and whether extramarital sex was always wrong (yes. no). Of the respondents, 144 said yes on both. 86 said no on both, 243 said no on prenantal and yes on extramarital, and 2 said yes on premarital and no
50 A short questionnaire measunng anxiety is given to a random sample of two students taken from a large introductory statistics class. Anxiety is measured both before and after the students take a midterm exam in statistics The scores are 91 before and 80 after for student I and 69 before and 60
51. A pool of six candidates for three managenal positions includes three feinales and three males Table 7.20 shows the results.a) Denote the three females by F, F. F and the three males by M. M2, M3. Identify the 20 distinct samples of size three that can be chosen from these six individualsb)
52. Refer to Problem 7 10 Suppose the same 1600 people who were interviewed in January were interviewed again in February. with the results shown in Table 7.21 TABLE 7.21 February January Approve Disapprove Total Approve 794 86 880 Disapprove Total 150 570 720 944 656 1600a) Test for a difference
53. Provide an example of a situation in which it is more sensible to compare means using dependent samples than independent samples. In Problems 7 54-7 56. select the conect response(s)
54. A 99% confidence interval for the difference between the proportions of men and women in Florida who are alcoholics equals (.02, .09).a) We are 99% confident that the proportion of alcoholics is between .02 and .09.b) We are 99% confident that the proportion of men in Florida who are alcoholics
55. To compare the population mean annual incomes for Hispanics (#41) and for whites (u) having jobs in construction, we construct a 95% confidence interval for -Mj.a) If the confidence interval is (3000, 6000). then at this confidence level we conclude that the inean income for whites is higher
56. For small samples, the Wilcoxon test differs from parametric procedures (for means) in the sense thata) The alternative hypothesis cannot be one-sidedb) It is unnecessary to assume that the population distribution is normalc) Random sampling is not assumedd) It applies directly to ordinal as
57. * A test consists of 100 true-false questions Joe did not study, so on each question, he randomly 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) Jane studied
58. Using their formulas, for independent samples show that oy, is larger than by, or oy, for either mean separately Provide some intuition for why this happens. (Hint: Notice that if Y is above (below), and I is below (above) 2, then Y2 - Y1 is even further below (above) 2-1. Thus there is the
59. *Let X, denote the observation for the ith subject at time 1. Let Y, denote the observation for the ith subject at time 2. Let D; Y;- X;.a) Letting X, Y. and D denote the means of these observations, show that =- X.b) Is the median difference (i.e.. the median of the D; values) equal to the
1 A Gallup Poll in 1995 suggested that in the United States. about 15% of males and 15% of females believe that abortion should be illegal in all circunstances (The Gallup Poll Monthly, No 354. Princeton, NJ: The Gallup Poll, March 1995, p. 30).a) For males and for females, report the conditional
2. Whether a woman becomes pregnant in the next year is a categorical variable with cate- gones (ves. no), and whether she and her partner use contraceptives is another categoncal vanable with categones (yes, no). Would you expect these variables to be statistically in- dependent, or associated?
3. For a sample of 100.000 subjects, Table 8.22 cross-classifies whether a subject is HIV+ by whether a diagnostic test for HIV+ status is positive (i.e.. indicates that the subject is HIV+).a) Construct the conditional distributions for the test result, given the true discase status.b) For those
4 In an article about crime in the United States, Newsweek magazine (January 10, 1994) quoted FBI statistics stating that of all blacks slain in 1992, 94% were slain by blacks, and of all whites slain in 1992. 83% were slain by whites. Let Y denote race of victim and X denote race of murderer.a)
5. A young child wonders what causes women to have babies. For each woman who lives on hier block, she observes whether her hair is gray and whether she has young children, with the results shown in Table 8.23.a) Construct the 2 x 2 contingency table that cross-classifies "gray hair" (yes, no) with
6. How large a x-value provides a P-value of .05 for testing independence for the following table dimensions"a) 2 2b) 3 x 3c) 2 x 5d) 5 x 5c) 39
7 Show that the contingency table in Table 8.24 has four degrees of freedoin, by filling in the missing cell counts TABLE 8.24 10 20 30 40 50 50 TABLE 8.25 100 88 60 Cigaretic Use Yes No Alcohol Yes Use Source. 1449 500 No 46 281 80 70 Study conducted by Wright State University School of Medicine
8. Table $ 25 refers to a survey conducted in 1992 of senior high school students in Dayton. Ohioa) Construct conditional distributions that treat cigarette smoking as the response vari- able. Interpret.b) Construct conditional distributions that treat alcohol use as the response variable. In-
9. Table 8 26 shows an SPSS printout for some analyses for a data set taken from the 1991 General Social Survey, with variables race and party identification.a) Form the conditonal distribution on party identification, for each race. Interpretb) Report the expected fiequency for the first cell, and
10 Table 8.27 is from the 1991 General Social Survey Subjects were asked their opinion about a man and woman having sex relations before marriage. They were also asked whether methods of birth control should be made available to teenagers between the ages of 14 and 16a) Software reports that x2 =
11. Refer to Problem 8.8.a) Describe the nature of the association using adjusted residuals.b) Describe the strength of association using the difference between users and nonusers of alcohol in the proportions who have used cigarettes. Interpret.c) Describe the strength of association using the
12. Table 8.28 refers to 68,694 passengers in autos and light trucha involved in accidents in the state of Maine in 1991. The table classifies passengers by whether they were wearing a seat belt and by whether they were injured or killed. Test the hypothesis of independence. Interpret the P-value.
13. Refer to the previous problem. Show how to follow up the test descriptively witha) An analysis using adjusted residualsb) The difference between two proportions.c) The odds ratio.
14. Table 8.29 refers to a national study of 15- and 16-year-old adolescents. The groups are four combinations of gender and race The event of interest is ever having sexual inter- course Is there an association between group and the response? Interpret the results in the computer printout supplied
15. Refer to the previous exercise.a) Describe the nature of the association, using conditional distributions.b) Describe the nature of the association for females, using adjusted residuals for the Yes category in the first two rows.c) Describe the strength of association. using the difference
16 Refer to the previous two exercisesa) Analyze the association between race and response, given gender, by conducting two chi-squared tests, one for females using the first two rows of the table and one for males using the last two rows of the table. Interpret.b) Analyze the overall association
17. Table 830 is from the 1991 General Social Survey White subjects were asked "If your party nominated a (Nego/Black) for President, would you vote for him if he were qual- ified for the job?" and "During the last few years, has anyone in your family brought a Inend who was a (Negro/Black) home
18. Refer to the previous exercise. Using the yes and no categories of each response, estimate the odds ratio. Interpret.
19. A new spaper article preceding the 1994 World Cup semifinal match between Italy and Bulgaria stated that "Italy is favored 10-11 to beat Bulgaria, which is rated at 10-3 to reach the final." Suppose this means that the odds that Italy wins are 11/10 = 1.1 and the odds that Bulgana wins are 3/10
20. According to data from the 1993 Substance Abuse and Mental Health Administration na- tional household survey on drug abuse, for Americans aged 26-34, 59% had used mari- Juana at least once in their lifetime, and 26% had used cocaine at least oncea) Find the odds of having used marijuana.
21. When asked by the National Opinion Research Center "Is there any area right around here that is, within a mile-where you would be afraid to walk alone at night"", in 1973 60% of females answered yes and 20% of males answered yes, whereas in 1994 60% of females answered yes and 30% of males
22. For murders in the the United States in 1993 having a single victim and single offender, Table 831 cross classifies the sex of the victim by the sex of the offender. Calculate and interpret the odds ratio. TABLE 8.30 TABLE 8.31 Black For Home For Dinner Sex of Sex of Victim President Yes No
23. According to the U.S Department of Justice, in 1994 the incarceration rate in the nation's prsons was 646 per 100.000 male residents. 45 per 100,000 female residents, 1471 per 100,000 black residents, and 207 per 100,000 white residents (Bureau of Justice Statistics Bulletin: Prisoners in

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