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 under study do receive, on average, salaries more than $4,000 per 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 programs 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 the nonprogram executives and x‾ = 55 and s = 8 for the program executives. All numbers are in thousands of dollars per year.
Conduct the test at α = 0.05, and evaluate the effectiveness of the programs in terms of increased average salary levels.