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

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.

https://brainmass.com/statistics/hypothesis-testing/hypothesis-test-significance-difference-means-17929

#### Solution Preview

Please refer to the attachment.

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

Let Md=Âµ2-Âµ1= (-$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 ...

#### 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.