Chapter 10, Problem 11PS

The annual NFL Super Bowl is the most widely watched sporting event in the United States each year. In recent years, there has been a great deal of interest in the ads that appear during the game. These ads vary in length with most lasting 30 seconds or 60 seconds. The SuperBowlAdScore represent the ad length and ad scores from a recent Super Bowl.

a. Assuming that the population variances from the 30-second ads and the 60-second ads are equal, is there evidence of a difference in the mean score between the two types of ads? $\text{(Use}\alpha =\mathrm{0.05.})$

b. Determine the p-value in (a) and interpret its meaning.

c. Assuming that the population variance from both types of ads are equal, construct and interpret a $95\%$ confidence interval estimate of the difference between the population mean score of the two types of ads.