Question

A study was carried out on the effectiveness of Reiki therapeutic touch to manage pain in cancer patients. Pain was assessed twice for each of the 17 cancer patients: once before and once after Reiki touch therapy. For each of the 17 subjects, the difference between each pair of pain scores was recorded (difference = after − before). The 17 differences have a mean of -1.83 and a standard deviation of 1.54.

1. Compute a 95% confidence interval for the true population mean change in pain scores.

(give answers to 4 places past decimal)

Answer 1

sample mean, xbar = -1.83
sample standard deviation, s = 1.54
sample size, n = 17
degrees of freedom, df = n - 1 = 16

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.12

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (-1.83 - 2.12 * 1.54/sqrt(17) , -1.83 + 2.12 * 1.54/sqrt(17))
CI = (-2.6218 , -1.0382)