Matched pairs t procedures Example 3 istening to Mozart improves students The taste test in Example 2 is in fact a matched pairs study in which the same 10 tasters rated before-and-after sweetness 迪过(cm甲A( Group B Diference Subject(co甲A(mBDa 371258.938350-24571 To compare the responses to the two 5641014435351.3 treatments in a matched pairs design, 37.9329.33 apply the one-sample t procedures to observed differences 747045487185.53580044 28?329420 1051236847-172421536747.06.67 1654051.101430 To analyze these data, subtract Group B The parameter u in a matched pairs t cores from group a scores for each procedure is the mean difference in the responses to the two treatments within matched pairs of subjects in the entire Step 1: Hypothesis. To assess whether population listening to Mozart significantly improved performance, we test HH 019 37 Matched pairs t procedures • The taste test in Example 2 is in fact a matched pairs study in which the same 10 tasters rated before-and-after sweetness. • To compare the responses to the two treatments in a matched pairs design, apply the one-sample t procedures to observed differences. 38 • The parameter in a matched pairs t procedure is the mean difference in the responses to the two treatments within matched pairs of subjects in the entire population. μ 20 39 Example 3 Subject Group A Group B Difference Subject Group A Group B Difference 1 30.60 37.97 -7.37 12 58.93 83.50 -24.57 2 48.43 51.57 -3.14 13 54.47 38.30 16.17 3 60.77 56.67 4.10 14 43.53 51.37 -7.84 4 36.07 40.47 -4.40 15 37.93 29.33 8.60 5 68.47 49.00 19.47 16 43.50 54.27 -10.77 6 32.43 43.23 -10.80 17 87.70 62.73 24.97 7 43.70 44.57 -0.87 18 53.53 58.00 -4.47 8 37.10 28.40 8.70 19 64.30 52.40 11.90 9 31.17 28.23 2.94 20 47.37 53.63 -6.26 10 51.23 68.47 -17.24 21 53.67 47.00 6.67 11 65.40 51.10 14.30 Listening to Mozart improves student’s performance on tests. 40 To analyze these data, subtract Group B scores from Group A scores for each subject. • Step 1: Hypothesis. To assess whether listening to Mozart significantly improved performance, we test 0 1 : 0 : 0 H H μ μ = >