- a. Construct and interpret an interval for which you are 95% confident that the population mean difference (dominant nondominant) in translation between dominant and nondominant arms for pitchers lies between the limits of the interval. b. Construct and interpret an interval for which you are 95% confident that the population mean difference (dominant nondominant) in translation between dominant and nondominant arms for position players lies between the limits of the interval. - C. Construct a two-sided interval for which you are 95% confident that the difference (pitchers - position players) of population mean difference (dominant - nondominant) on anteroposterior translation of shoulders of dominant and 5 nondominant arms between pitchers and position players lies between the limits of the interval. d. Do the data support the claim that the population mean translation for the dominant arms of pitchers is longer than that for the non-dominant arms at 0.05 level of significance? Write out the hypotheses and report your P-value. e. Do the data support the claim that pitchers have larger mean difference (dominant - nondominant) than position players in side-to-side anteroposterior translation of shoulders at 0.05 level of significance? Problem 10. Sethi, Paul Michael; Tibone, James E; and Lee, Thay Q. (2004, Quantitative assessment of glenohumeral translation in baseball players: a comparison of pitchers versus nonpitching athletes, The American Journal of Sports Medicine 32(7), 1711-1715) considered various of shoulder motion for a sample of pitchers and another sample of position players. The data on anteroposterior translation (mm), a measure of the extent of anterior and posterior motion, both for the dominant arm and nondominant arm are given as follows. Probability plots show that differences between dominant and nondominant arms for position players and pitchers follow normal distributions. Pos Dom Tr Pos ND Pit Dom Tr Pit ND Tr Tr 1 30.31 32.54 27.63 24.33 2 44.86 40.95 30.57 26.36 3 22.09 23.48 32.62 30.62 4 31.26 31.11 39.79 33.74 5 28.07 28.75 28.50 29.84 6 31.93 29.32 26.70 26.71 7 34.68 34.79 30.34 26.45 8 29.10 28.87 28.69 21.49 9 25.51 27.59 31.19 20.82 10 22.49 21.01 36.00 21.75 11 28.74 30.31 31.58 28.32 12 27.89 27.92 32.55 27.22 13 28.48 27.85 29.56 28.86 14 25.60 24.95 28.64 28.58 15 20.21 21.59 28.58 27.15 16 33.77 32.48 31.99 29.46 17 32.59 32.48 27.16 21.26 18 32.60 31.61 19 29.30 27.46 Mean 29.4463 29.2137 30.7112 26.6447 SD 5.4655 4.7013 3.3310 3.6679 Mean of Dom - ND 0.2326 Dom - ND 4.0665 SD of Dom - ND 1.6034 Dom - ND 3.9549