The 2014 General Social Survey asked 1475 subjects how many hours per day they watched TV, on average. Are there differences in population means according to the marital status of the subject (single, married, divorced)? The sample means were 3.27 for singles (n = 459), 2.64 for married subjects (n = 731), and 2.85 for divorced subjects (n = 285). In a one-way ANOVA, the between-groups estimate of the variance is 54.8 and the within-groups estimate is 6.0. (The dataset is available online as TV Hours 2014.)
a. Conduct the ANOVA test and make a decision using a 0.05 significance level.
b. The 95% confidence interval comparing the population means is (0.3, 0.9) for single and married subjects, (0.06, 0.8) for single and divorced subjects, and (-0.5, 0.1) for married and divorced subjects. 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 single and married subjects.
d. Refer to part c. Would the corresponding interval formed with the Tukey method be wider or narrower? Explain why.