Question

.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. (10marks)
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. Assume unequal variance.

Answer 1

Explanation:

a) The test statistic is (4.4-4)/(1.3/sqrt(70)) = 2.83. The p-value is 0.0023. Since the p-value is less than 0.05, we reject the null hypothesis.

b) The test statistic is (5.3-4.4)/sqrt((1.4^2/106)+(1.3^2/70)) = 4.09. The p-value is less than 0.0001. Since the p-value is less than 0.05, we reject the null hypothesis.