Advertisers fear that users of DVD recorders will "fast forward" past commercials when they watch a recorded program. A leading British pay television company told their advertisers that this effect might be offset because DVD users watch more TV. A sample of 15 DVD users showed a daily mean screen time of 2 hours and 26 minutes with a standard deviation of 14 minutes, compared with a daily mean of 2 hours and 7 minutes with a standard deviation of 12 minutes for a sample of 15 non-DVD users.
(a) Construct a 95 percent confidence interval for the difference in mean TV watching. Would this sample support the company's claim (i.e., is zero within the confidence interval for the mean difference)?
(b) Discuss any assumptions that are needed.