The 2008 General Social Survey asked 1324 subjects how many hours per day they watched TV, on the average. Are there differences in population means according to the race of the subject (white, black, other)? The sample means were 2.76 for whites (n = 1014), 4.38 for blacks (n = 188), and 2.70 for other (n = 122). In a one-way ANOVA, the between-groups estimate of the variance is 215.26 and the within-groups estimate is 6.76.
a. Conduct the ANOVA test and make a decision using 0.05 significance level.
b. The 95% confidence interval comparing the population means is (1.1, 2.2) for blacks and whites, (-0.4, 0.5) for whites and the other category, and (1.0, 2.4) for blacks and the other category. Based on the three confidence intervals, indicate which pairs of means are significantly different. Interpret.
c. Based on the information given, show how to construct the confidence interval that compares the population mean TV watching for blacks and whites.
d. Refer to part c. Would the corresponding interval formed with the Tukey method be wider, or narrower? Explain why.