One type of experiment that might be performed by an
One type of experiment that might be performed by an exercise physiologist is as follows: Each person in a random sample is tested in a weight room to determine the heaviest weight with which he or she can perform an incline press five times with his or her dominant arm (defined as the hand that a person uses for writing). After a significant rest period, the same weight is determined for each individual’s non-dominant arm. The physiologist is interested in the differences in the weights pressed by each arm. The following data represent the maximum weights (in pounds) pressed by each arm for a random sample of 18 fifteen-year old girls. Assume that the differences in weights pressed by each arm for all fifteen year old girls are approximately normally distributed.
a. Make a 99% confidence interval for the mean of the paired differences for the two populations, where a paired difference is equal to the maximum weight for the dominant arm minus the maximum weight for the non-dominant arm.
b. Using a 1% significance level, can you conclude that the average paired difference as defined in part a is positive?
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