www.downloadslide.com Exercises 727 2004 presidential election. Voters were asked how often they attended church services and which of the two major presidential candidates (George W. Bush or John Kerry) they intended to vote for in the election. The results of a similar survey are contained in the following table. 6 Church Attendance Bush Kerry More than once per week 89 53 Once per week 87 68 Once or twice per month 93 85 Once or twice per year 114 134 Seldom/never 22 36 a b Is there sufficient evidence to indicate dependence between reported frequency of church attendance and choice of presidential candidate in the 2004 presidential election? Test at the .05 level of significance. Place bounds on the attained significance level. Give a 95% confidence interval for the proportion of individuals who report attending church at least once per week. 14.17 In the academic world, students and their faculty supervisors often collaborate on research papers, producing works in which publication credit can take several forms. Many feel that the first authorship of a student’s paper should be given to the student unless the input from the faculty advisor was substantial. In an attempt to see whether this is in fact the case, authorship credit was studied for several different levels of faculty input and two objectives (dissertations versus nondegree research). The frequency of authorship assignment decisions for published dissertations is given in the accompanying tables as assigned by 60 faculty members and 161 students: 7 Faculty respondents Authorship Assignment High Input Medium Input Low Input Faculty first author, student mandatory 4 0 0 second author Student first author, faculty mandatory 15 12 3 second author Student first author, faculty courtesy 2 7 7 second author Student sole author 2 3 5 Student respondents Authorship Assignment High Input Medium Input Low Input Faculty first author, student mandatory 19 6 2 second author Student first author, faculty mandatory 19 41 27 second author Student first author, faculty courtesy 3 7 31 second author Student sole author 0 3 3 6. Source: Adapted from Bettye Wells Miller, “Faith Shows Ballot Clout,” Press-Enterprise (Riverside, Calif.), 1 March 2004, p. A7. 7. Source: M. Martin Costa and M. Gatz, “Determination of Authorship Credit in Published Dissertations,” Psychological Science 3(6) (1992): 54.
www.downloadslide.com 728 Chapter 14 Analysis of Categorical Data a b c Is there sufficient evidence to indicate a dependence between the authorship assignment and the input of the faculty advisor as judged by faculty members? Test using α = .01. Is there sufficient evidence to indicate a dependence between the authorship assignment and the input of the faculty advisor as judged by students? Test using α = .01. Have any of the assumptions necessary for a valid analysis in parts (a) and (b) been violated? What effect might this have on the validity of your conclusions? 14.18 A study of the amount of violence viewed on television as it relates to the age of the viewer yielded the results shown in the accompanying table for 81 people. (Each person in the study was classified, according to the person’s TV-viewing habits, as a low-violence or high-violence viewer.) Do the data indicate that viewing of violence is not independent of age of viewer, at the 5% significance level? Age Viewing 16–34 35–54 55 and Over Low violence 8 12 21 High violence 18 15 7 14.19 The results of a study 8 suggest that the initial electrocardiogram (ECG) of a suspected heart attack victim can be used to predict in-hospital complications of an acute nature. The study included 469 patients with suspected myocardial infarction (heart attack). Each patient was categorized according to whether their initial ECG was positive or negative and whether the person suffered life-threatening complications subsequently in the hospital. The results are summarized in the following table. Subsequent In-Hospital Life-Threatening Complications ECG No Yes Total Negative 166 1 167 Positive 260 42 302 Total 426 43 469 a b Is there sufficient evidence to indicate that whether or not a heart attack patient suffers complications depends on the outcome of the initial ECG? Test using α = .05. Give bounds for the observed significance level. 14.20 Refer to Exercise 14.10. Test the hypothesis, at the 5% significance level, that the type A defects occur independently of the type B defects. 14.21 An interesting and practical use of the χ 2 test comes about in testing for segregation of species of plants or animals. Suppose that two species of plants, A and B, are growing on a test plot. To assess whether the species tend to segregate, a researcher randomly samples n plants from the plot; the species of each sampled plant, and the species of its nearest neighbor are recorded. The data are then arranged in a table, as shown here. 8. Source: J. E. Brush et al., “Use of the Initial Electrocardiogram to Predict In-Hospital Complications of Acute Myocardial Infarction,” New England Journal of Medicine (May 1985).