Independent random samples of business managers and college economics faculty were asked to respond on a scale from 1 (strongly disagree) to 7 (strongly agree) to this statement: Grades in advanced economics are good indicators of students' analytical skills. For a sample of 70 business managers, the mean response was 4.4 and the sample standard deviation was 1.3. For a sample of 106 economics faculty the mean response was 5.3 and the sample standard deviation was 1.4.
a. Test, at the 5% level, the null hypothesis that the population mean response for business managers would be at most 4.0.
b. Test, at the 5% level, the null hypothesis that the population means are equal against the alternative that the population mean response is higher for economics faculty than for business managers.