MATH SOLVE

4 months ago

Q:
# A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain scale before and after hypnosis. Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. Construct 95% confidence interval for the mean of the "before−after" differences. Does hypnotism appear to be effective in reducing pain?Before 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8After 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7

Accepted Solution

A:

Required data:Before 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8After 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7Answer:Confidence interval = (-0.404 ; 1.804)Pvalue = 0.178Step-by-step explanation:H0: μd = 0H1 : μd ≠ 0Difference, d = (x - y)d = - 0.3, 0.2, 0.3, 2.4, 3.1, - 0.6, 0.4, 0.1Using calculator :μd = 0.7Sd = 1.32Confidence interval :Mean ± margin of error Margin of Error =Tcritical * Sd/√nTcritical at df = 7, 0.5, 2 - tailed = 2.365Margin of Error = 2.365 * 1.32/√8Margin of Error = 1.104Lower boundary :(0.7 - 1.104) = - 0.404Upper boundary :(0.7 + 1.104) = 1.804(-0.404 ; 1.804)Test statistic, = μd / (Sd ÷ √n)Test statistic = 0.7 / (1.32 ÷ √8) Test statistic = 1.499From the test statistic score ; using a Pvalue calculator :Pvalue = 0.178 ( 3 decimal places)