Question: #10.79: An article in The New York Times (A. Jennings, “What’s good for a Busienss Can be Hard on Friends,” The New York Times, August 4, 2007, pp. C1-C2) reported that according to a poll, the mean number of cellphone calls per month was 290 for 18- to 24-year-old and 194 for 45- to 54-year-olds, whereas the mean number of text messages per month was 290 for 18- to 24-year-olds and 57 for 45- to 54-year-olds. Suppose that the poll was based on a sample of 100 18-to 24-year-olds and 100 45- to 54-year-olds, and that the standard deviation of the number of cellphone calls per month was 100 for 18-to 24-year-olds and 90 for 45- to 54-year-olds, whereas the standard deviation of the number of text messages per month was 90 for 18- to 24-year-olds and 77 for 45- to 54-year olds

Use a level of significance of 0.05.

a) Is there evidence of a difference in the variances of the number of cellphone calls per month for 18- to 24-year-olds and 45- to 54-year-olds?

b) Is there evidence of a difference in the mean number of cellphone calls per month for 18- to 24-year-olds and 45- to 54-year olds?

c) Construct and interpret a 95% confidence interval estimate of the difference in the mean number of cellphone calls per month for 18- to 24-year-olds and 45- to 54-year-olds.

d) Is there evidence of a difference in the variances of the number of text messages per month for 18- to 24-year-olds and 45- to 54-year olds?

e) Is there evidence of a difference in the mean number of text messages per month for 18- to 24-year-olds and 45- to 54-year olds?

f) Construct and interpret a 95% confidence interval estimate of the difference in the mean number of text messages per month for 18- to 24-year-olds and 45- to 54-year olds.

g) Based on the results of (a) through (f), what conclusions can you make concerning cellphone and text message usage between 18- to 24-year-olds and 45- to 54-year olds?