The paper "Quantitative Assessment of Glenohumeral Translation in Baseball Players" (The American Journal of Sports Medicine [2004]: 1711–1715) considered various aspects of shoulder motion for a sample of pitchers and another sample of position players. The authors kindly supplied the data on the following page on anteroposterior translation (mm), a measure of the extent of anterior and posterior motion, both for the dominant arm and the nondominant arm.

a. Estimate the true average difference in translation between dominant and nondominant arms for pitchers using a 95% confidence interval.
b. Estimate the true average difference in translation between dominant and nondominant arms for position players using a 95% confidence interval.
c. The authors asserted that pitchers have greater difference in mean anteroposterior translation of their shoulders than do position players. Do you agree? Explain.