In a study designed to test the effectiveness of acupuncture

In a study designed to test the effectiveness of acupuncture for treating migraine, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine attacks for acupuncture treatment group had a mean of 1.8 and a standard deviation of 1.4. The numbers of migraine attacks for the sham treatment group had a mean of 1.6 and a standard deviation of 1.2. 1. Construct a 95% confidence interval estimate of the mean number of migraine attacks for those treated with acupuncture. 2. Interpret this interval in the context of this problem.

Solution

1. Construct a 97% confidence interval estimate of the mean number of migraine attacks for those treated with acupuncture.

Given a=1-0.97=0.03, Z(0.03/2)= Z(0.015) =2.17 (from standard normal table)

So the lower bound is

xbar- Z*s/vn =1.8-2.17*1.4/sqrt(142) =1.545057

So the upper bound is

xbar+ Z*s/vn =1.8+2.17*1.4/sqrt(142) =2.054943

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2. Interpret this interval in the context of this problem.

We have 97% confident that the population mean will be within this interval.

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3. Construct a 97% confidence interval estimate of the mean number of migraine attacks for those given a sham treatment.

So the lower bound is

xbar- Z*s/vn =1.6-2.17*1.2/sqrt(80) =1.308864

So the upper bound is

xbar+ Z*s/vn =1.6+2.17*1.2/sqrt(80) =1.891136

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4. Interpret this interval in the context of this problem.

We have 97% confident that the population mean will be within this interval.

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5. Compare the two confidence intervals. Do the results suggest the effectiveness of one method over the other?

No, because these two confidence interval are overlap.