Three Universities in Your State Decided to Administer the Same $\alpha$

Essay

Three universities in your state decided to administer the same comprehensive examination to the recipients of MBA degrees from the three institutions. From each institution, MBA recipients were randomly selected and were given the test. The following table shows the scores of the students from each university.

At $\alpha$ = 0.01, test to see if there is any significant difference in the average scores of the students from the three universities. (Note that the sample sizes are not equal.) Use both the critical and p-value approaches.