55. If you go to a major league baseball game, how long do you expect the game to be? From the 2429 games played in 2001, here is a random sample of 25 times in minutes:

352 150 164 167 225 159 142 182 229 163 188 197 189 235 161 195 177 166 195 160 154 130 189 188 225 This is one of those rare instances in which we can do a con dence interval and compare with the true population mean. The mean of all 2429 lengths is 178.29 (almost three hours).

a. Compute the t-based con dence interval of Section 8.3.

b. Use a normal plot to see if part

(a) is valid.

c. Generate a bootstrap sample of 1000 means.

d. Use the standard deviation for part

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

e. Investigate the distribution of the bootstrap means to see if part

(d) is valid.

f. Use part

(c) to form the 95% con dence interval using the percentile method.

g. Say which interval should be used and explain why. Does your interval include the true value, 178.29?