According to the U.S. Postal Service, the average weight of mail received by Americans in 2011through the Postal Service was 57.2 pounds (The New York Times, December 4, 2011). One hundred randomly selected Americans were asked to keep all their mail for last year. It was found that they received an average of 55.3 pounds of mail last year. Suppose that the population standard deviation is 8.4 pounds.
a. Find the p-value for the test of hypothesis with the alternative hypothesis that the average weight of mail received by all Americans last year was less than 57.2 pounds. Will you reject the null hypothesis at α = .01? Explain. What if α = .025?
b. Test the hypothesis of part a using the critical-value approach. Will you reject the null hypothesis at α = .01? What if α = .025?