The comedian Kevin Hart famously jokes about his short stature, even naming his first ever comedy tour “I’m a Grown Little Man.” To build publicity for his latest tour, Hart decides to hold a contest between two towns, Smallville and Anytown, for a free performance open only to residents of the winning town.

The winning town will have the lower average height of the men who live in the town. Random samples of seventy-five men are drawn from each town.

The mean height of the Smallville sample is 68 inches, and it is 69 inches for Anytown. The standard deviations are 2 inches for Smallville and 3.75 inches for Anytown.

a. Find the 80% confidence intervals for the mean height of men in both towns.

b. Give the range of each town’s confidence interval.

c. Is there a winner of the contest, according to these confidence intervals?