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?

Transcribed Image Text:

Nondominant Dominant Arm 47 40 Nondominant Dominant Arm Subject 10 Subject 53 35 32 27 12 21 25 20 12 15 12 29 32 14 17 18