Answer Happy

Mail- Let's use the data from Example 11.5 to estimate the difference in mean range of motion prior to treatment and the mean range of motion after ultrasound and stretch treatment for physical therapy patients. The data and the computed differences are shown in the accompanying table Round 7 Range of Motion Subject 1 23 4 5 6 7 Pre-treatment 31 53 45 57 SO 43 32 Post-treatment 32 46 64 49 45 40 Difference -1 -6 -1 1-2-3 We will use these data to estimate the mean change in range of motion using a 95% confidence interval, assuming that the patients participating in this study can be considered as representative of physical therapy patients. The following boxplot of the sample differences is not inconsistent with a difference population that is approximately normal, so the paired confidence interval is appropriate 59 -1 The mean and standard deviation computed using the seven sample differences are -3.43 and 3.51, respectively. The t critical value for of 6 and a 95% confidence level is 2.45, and therefore the confidence intervat is 3.51 *+ (t critical value) -3.43 + (2.45) Vn Vi -3.43 +3.25 = (-6,68,-0.18) Based on the sample data, we can be 95% confident that the difference in mean range of motion is between -6.68 and -0.18. That is, we are 95% confident that the mean increase in range of motion after ultrasound and stretch therapy is somewhere between 0.18 and 6.68. MINITAB output is also shown. MINITAB carries a bit more decimal accuracy, and reports a 95% confidence interval of ( -6.67025, -0.18690). Paired T-Test and CI: Pre, Post Paid Tor Pre-Post N Mean Pre 7 49.4286 FONE 47.8573 Diference 7 -3.42557 Stev 9.9976 10.8847 >.50510 SE Mean 3.7787 4.114 280

The mean and standard deviation computed using the seven sample differences are -3.43 and 3.51, respectively. The t critical value for df - 6 and a 95% confidence level is 2.45, and therefore the confidence interval is 3.51 *g* (t critical value) -3.43 + (2.45) Vn V7 13.43 43.25 -(-6.68,-0.18) Based on the sample data, we can be 95% confident that the difference in mean range of motion is between -6.68 and -0.18. That is, we are 99% confident that the mean increase in range of motion after ultrasound and stretch therapy is somewhere between 0.19 and 6,68, MINITAB output is also shown. MINITAB carries a bit more decimal accuracy, and reports a 95% confidence interval of (-6.67025, -0.18690) Daired 7-Test and cr: Pre, Post Paired T for Pre-Post Mean Stev SE Moon pre 14.4206 9.9976 3.7707 Pont 17 47.8571 10.0142 4.1140 Diference 2 -3.42857 2.50510 1.32400 956 ct for mean difference 4.67025, -0.10690) T-Test of mean difference -O (V not - 0) T Value - 2:59 Value - 0.041 Suppose that for the 7 differences, the mean was -4.75, and thes, was still 3.50510. Calculate the test statistic -3.59 -2.59 -9.49 -4.75 Calculate a 95% confidence interval for the this mean difference. (Round your answers to two decimal places.)