Suppose a student organization at the University of Illinois would like to test for a difference in class sizes between the business and engineering 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. Recall that testing for a difference between two population means requires an assumption about population variances. Perform a hypothesis test using α = 0.05 to determine if the population variance for class size is different for these two departments.

b. Verify your results using PH_Stat.

c. Identify the p value from part b and interpret the result.