David Anderson has been working as a lecturer at Michigan State University for the last three years. He teaches two large sections of introductory accounting every semester.
While he uses the same lecture notes in both sections, his students in the first section outperform those in the second section. He believes that students in the first section not only tend to get higher scores, they also tend to have lower variability in scores.
David decides to carry out a formal test to validate his hunch regarding the difference in average scores.
In a random sample of 18 students in the first section, he computes a mean and a standard deviation of 77.4 and 10.8, respectively.
In the second section, a random sample of 14 students results in a mean of 74.1 and a standard deviation of 12.2.
a. Construct the null and the alternative hypotheses to test David's hunch.
b. Compute the value of the test statistic. What assumption regarding the populations is necessary to implement this step?
c. Implement the test at α = 0.01 and interpret your results.