Suppose a student organization at a university collected data for a study involving class sizes from different departments. The following table shows the average class size from a random sample of classes in the business school vs. the average class size from a random sample of classes in the engineering school. Data for the sample sizes and standard deviations are also shown.

Business Engineering

Sample mean38.5 30.1

Sample standard deviation 10.1 13.2

Sample size 15 14

a. Perform a hypothesis test using =0.01to determine if the average class size differs between these departments. Assume the population variances for the number of students per class are not equal.

The test statistic is

The critical value is

The P- Value is