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 97% 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.

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

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

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

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.