A leading manufacturer of exercise equipment wanted to collect data on the effectiveness of their equipment. An August 2001 article in the journal Medicine and Science in Sports and Exercise compared how long it would take men and women to burn 200 calories during light or heavy workouts on various kinds of exercise equipment. The results summarized in the table are the average times for a group of physically active young men and women whose performances were measured on a representative sample of exercise equipment.

a) On average, how many minutes longer than a man must a woman exercise at a light exertion rate in order to burn 200 calories? Find a 95% confidence interval.
b) Estimate the average number of minutes longer a woman must work out at light exertion than at heavy exertion to get the same benefit. Find a 95% confidence interval.
c) These data are actually averages rather than individual times. How might this affect the margins of error in these confidence intervals?

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AVERAGE MIMUTESTO BURM 200 CAORIES Light Exertion Hard Exertion Men Women en Women Treadmill 12 12 13 14 14 S X-CSkier 16 18 Stair Climber Rowing Machine Exercise Rider Exercise Bike 21 27 29 37 25 36 24 20 16