Do males and females differ in the amount of time they talk on the phone and the number of text messages they send? A study reported that women spent a mean of 818 minutes per month talking as compared to 716 minutes per month for men. (Data extracted from "Women Talk and Text More," USA Today, February 1, 2011, p. 1A.) The sample sizes were not reported. Suppose that the sample sizes were 100 each for women and men and that the standard deviation for women was 125 minutes per month as compared to 100 minutes per month for men.
a. Using a 0.01 level of significance, is there evidence of a difference in the variances of the amount of time spent talking between women and men?
b. To test for a difference in the mean talking time of women and men, is it most appropriate to use the pooled-variance t test or the separate-variance t test? Use the most appropriate test to determine if there is a difference in the amount of time spent talking between women and men.
The article also reported that women sent a mean of 716 text messages per month compared to 555 per month for men. Suppose that the standard deviation for women was 150 text messages per month compared to 125 text messages per month for men.
c. Using a 0.01 level of significance, is there evidence of a difference in the variances of the number of text messages sent per month by women and men?
d. Based on the results of (c), use the most appropriate test to determine, at the 0.01 level of significance, whether there is evidence of a difference in the mean number of text messages sent per month by women and men.