56. The median might be a more meaningful statistic for the length-of-game data in Exercise 55. The median of all 2429 lengths is 175 minutes.

a. Obtain a bootstrap sample of 1000 medians.

b. Use the standard deviation for part

(a) to get a 95% con dence interval for the population median.

c. Investigate the distribution of the bootstrap medians and discuss the validity of part (b). Does the distribution take on just a few values?

d. Use part

(a) to form a 95% con dence interval for the median using the percentile method. Compare your answer with the population median, 175.

e. Comparing the percentile intervals for the mean and the median, is there much difference in their widths? If not, and you are forced to choose between them for the length-of-game data, which do you choose and why?