Question
In a study designed to test the effectiveness of acupunture for treating migraine, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine attacks for the acupuncture treatment group had a mean of 1.8 and a standard deviation of 1.4. The numbers of migrain attacks for the sham treatment group had a mean of 1.6 and a standard deviation of 1.2.<BR><BR>Construct a 95% confidence interval estimate of the mean number of migrain attacks for those treated with acupuncture.<BR><BR>Construct the 95% confidence interval estimate of the mean number of migrain attacks for those given a sham treatment.<BR><BR>Compare the two confidence intervals. What do the results sugggest about the effectiveness of acupuncture?
Explanation / Answer
acupunture : sample size, n = 142 mean , µ = 1.8 standard deviation , s = 1.4 standard error, e = s/vn = 1.4/v142 =0.1175 at a 95% confidence , for a two tail distribution, z = 1.96 (from z table) interval estimate of the mean number of migrain attacks for those treated with acupuncture = µ ± (z*e) = 1.8 ± (1.96*0.1175) =(1.5697, 2.0303) sham treatment: sample size, n = 80 mean , µ = 1.6 standard deviation , s = 1.2 standard error, e = s/vn = 1.2/v80 =0.1342 at a 95% confidence , for a two tail distribution, z = 1.96 (from z table) the 95% confidence interval estimate of the mean number of migrain attacks for those given a sham treatment = µ ± (z*e) = 1.2 ± (1.96*0.1342) =(0.94, 1.46) mean , µ = 1.6 standard deviation , s = 1.2 standard error, e = s/vn = 1.2/v80 =0.1342 at a 95% confidence , for a two tail distribution, z = 1.96 (from z table) the 95% confidence interval estimate of the mean number of migrain attacks for those given a sham treatment = µ ± (z*e) = 1.2 ± (1.96*0.1342) =(0.94, 1.46)