Do young children use cell phones? Apparently so, according to a recent study (A. Ross, "Message to Santa; KidsWant a Phone," Palm Beach Post, December 16, 2008, pp. 1A, 4A), which stated that cell phone users under 12 years of age averaged 137 calls per month as compared to 231 calls per month for cell phone users 13 to 17 years of age. No sample sizes were reported. Suppose that the results were based on samples of 50 cell phone users in each group and that the sample standard deviation for cell phone users under 12 years of age was 51.7 calls per month and the sample standard deviation for cell phone users 13 to 17 years of age was 67.6 calls per month.
a. Assuming that the variances in the populations of cell phone users are equal, is there evidence of a difference in the mean cell phone usage between cell phone users under 12 years of age and cell phone users 13 to 17 years of age? (Use a 0.05 level of significance.)
b. In addition to equal variances, what other assumption is necessary in (a)?