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find confidence interval with margin of error

I need help with the following questions:

1. A simple random sample of 40 salaries of NCAA football coaches has a mean of $415,953 and a standard deviation of $463,364.
Construct a 95% confidence interval estimate of the mean salary of an NCAA football coach.
2. 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 the 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.
a. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those treated with acupuncture.
b. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those given a sham treatment.
c. Compare the two confidence intervals. What do the results suggest about the effectiveness of acupuncture?

Solution Preview

1. The critical value for 95% confidence interval is 1.96 (n>30, we could use either critical z score or t score)
Margin of error=critical value*standard ...

Solution Summary

The solution provides detailed explanation as to how to find out the confidence interval with margin of error.

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