Question: The Bath Heritage Days, which take place in Bath, Maine, have been popular for, among other things, an eating contest. In 2009, the contest switched from blueberry pie to a Whoopie Pie (www.timesrecord.com), which consists of two large, chocolate cake-like cookies filled with a large amount of vanilla cream. Sixty-five randomly selected adults are chosen to eat a 1-pound Whoopie Pie, and the average time for 59 adults (out of these 65) is 127.10 seconds. Based on other Whoopie Pie-eating contests throughout the United States, suppose that the standard deviation of the times taken by all adults to consume 1-pound Whoopie pies are known to be 23.80 seconds.
a. Find the p-value for the test of hypothesis with the alternative hypothesis that the mean time to eat a 1-pound Whoopie Pie is more than 2 minutes. Will you reject the null hypothesis at Explain. What if α = .02?
b. Test the hypothesis of part a using the critical-value approach. Will you reject the null hypothesis at α = .01? What if α = .02?