(a) Is it plausible that the heights are normally distributed with a mean of 70 inches and a standard deviation of 2 inches?
(b) Is it plausible that the heights are normally distributed with a mean of 71 inches and a standard deviation of 1 inch?
(c) Consider the null hypothesis that the median height is 70 inches. What statistic is used by the sign test procedure to test this null hypothesis? What is the p-value?
(d) Test the null hypothesis in part (e) using the signed rank test.
(e) Use the sign test, the signed rank test, and the t-test to obtain 95% confidence intervals on the median (or mean) service time. What assumptions are required by these three test procedures? Do the assumptions seem appropriate? How would you summarize your results?