Suppose a student organization at the University of Illinois collected data for a study involving class sizes from different departments. A random sample of 11 classes in the business department had an average size of 38.1 students with a sample standard deviation of 10.6 students. A random sample of 12 classes in the engineering department had an average size of 32.6 students with a sample standard deviation of 13.2 students.

a. Perform a hypothesis test using α = 0.05 to determine if the average class size differs between these departments. Assume the population variances for the number of students per class are not equal.

b. Approximate the p value using Table 5 in Appendix A and interpret the results.

c. Determine the precise p value using Excel.

d. Verify your results using PHStat.

e. What assumptions need to be made in order to perform this procedure?