Question: Business schools at certain prestigious universities offer nondegree management training programs for high-level executives. These programs supposedly develop executives’ leadership abilities and help them advance to higher management positions within 2 years after program completion. A management consulting firm wants to test the effectiveness of these programs and sets out to conduct a one-tailed test, where the alternative hypothesis is that graduates of the programs of the programs under study do receive, on average, salaries more than $4,000 a year higher than salaries of comparable executives without the special university training. To test the hypotheses, the firm traces a random sample of 28 top executives who earn, at the time the sample is selected, about the same salaries. Out of this group, 13 executives randomly selected from the group of 28 executives are enrolled in one of the university program under study. Two years later, average salaries for the two groups and standard deviations of salaries are computed. The results are x = 48 and s= 6 for nonprogram executives and x=55 and s=8for the program executives. All numbers are in the thousands of dollars per year. Conduct a test at α = 0.05 and evaluate the effectiveness of the programs terms of increased average salary levels.