A company psychologist wanted to test if company executives have job-related stress scores higher than those of university professors. He took a sample of 40 executives and 50 professors and tested them for job-related stress. The sample of 40 executives gave a mean stress score of 7.6. The sample of 50 professors produced a mean stress score of 5.4. Assume that the standard deviations of the two populations are .8 and 1.3, respectively.
a. Construct a 99% confidence interval for the difference between the mean stress scores of all executives and all professors.
b. Test at a 2.5% significance level whether the mean stress score of all executives is higher than that of all professors.