Your radio station, which has generally targeted the so-called baby-boomers, is starting to reorient its programming to a younger audience. Formats have been changed, some new on air personalities have been hired, and generally efforts have been made to come up with a fresh approach. Now the radio station wants to see whether these efforts have been successful in reaching a younger audience. In the past, the average listener age was 48.2.
a. What null and alternative hypotheses would be appropriate here?
b. Explain the Type I and Type II errors in the context of the radio audience.
c. Suppose you rejected the null hypothesis with a p-value of 1%. What does this tell you? Does it mean the radio station has accomplished its goal?
d. Suppose the situation described in part c occurs, and the sample mean is 46. Does this mean the radio station has accomplished its goal?