Question: 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 nondominant 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 fifteenyear 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 nondominant arm.
b. Using the 2% significance level, can you conclude that the average paired difference as defined in part a is positive?