# A hypothesis test to determine if there is a significant difference in means across two groups.

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The American Association of University Professors conducts salary studies of college professors and publishes its finding in the AAUP Annual Report. College professors are divided into two populations: faculty in public institutions and faculty in private institutions. The summary statistics for the starting salaries of the two populations are given below. Use the traditional method to test for a difference in the means of the two groups at the 0.02 level of significance. Find the 98% confidence interval for the difference between the two means and interpret the result.

Institution

Sample 1:Public mean -$33,890 sd-$1,820 n-37

Sample 2: Private mean- $32,610 sd-$1,730 n-35.

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##### Solution Summary

The following outlines the process for determining if there is a significant difference in means across two groups. Additionally a 98% confidence interval is calculated.

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Please refer to the attachment.

Find the 98% confidence interval for the difference between the two means

Let Md=µ2-µ1= (-$32,610) - (-$33,890)= 1280

Applying the general formula,

The estimated standard error , is computed assuming that the variances in the two populations are equal. when n1 n2. The first difference is that MSE is computed differently. If the two values ...

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