An annual race director records an average finish time of 12.3 min over many years of results. Runners are not permitted to run the same race twice, so each new year features a new crop of runners. This year’s race by 51 runners completed the course in an average of 12.1 min, with a standard deviation (using n − 1) of 1.2 min.

a. State the nondirectional hypothesis.

b. Determine the critical t for a = .05.

c. Calculate t using the sample standard deviation as the estimated population standard deviation. Show your work.

d. Did this year’s runners complete the race in a significantly different time from previous years’ runners?