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Advertisers examine the average age of viewers of TV programs. For example, 60 Minutes reportedly has one of the highest average ages at 57. Suppose that a marketing analyst believes that the age gap between 60 Minutes and Star Trek: Voyager has narrowed to less than the historical 15 years. A random sample of 100 viewers from each of the TV programs was selected and the results are as follows:
60 Minutes: Sample Mean = 55.6 Population standard deviation = 10.8, Sample size = 100. Star Trek: Voyager: Sample Mean = 41.8, Population standard deviation = 7.9, Sample size = 100.
A. Construct a 99% confidence interval on the difference of the average ages for the viewers of the two TV programs. How can you interpret this interval?
B. Test the hypothesis that the difference in the average age of viewers for these two programs is less than 15 years. Use a significance level of 1%.
C. Why can you not use the confidence interval in part A to test the hypothesis in part B?
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