Suppose the student union at BCIT collected normally distributed data for a study involving class sizes from different departments. A random sample of 11 classes in the mathematics 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 physics department had an average size of 32.6 students with a sample standard deviation of 13.2 students.

(a) Perform a hypothesis test using = 0.05 to determine if the average class size differs between these departments.

(b) Find the 98% confidence interval for the difference between the average class sizes.