Three universities administer the same comprehensive examination to the recipients of MS degrees in psychology. From each institution, a random sample of MS recipients was selected, and these recipients were then given the exam. The following table shows the scores of the students examined by each university. Note that the sample sizes are not equal. University A University B University C 90 61 81 96 94 69 76 90 89 93 79 78 98 65 89 (a) Compute the overall mean I. (b) At a = 0.01, test to see if there is any significant difference in the average scores of all the students who took the exam from the three universities. Use both the critical value and p-value approaches. (Let population 1 be all MS recipients from university A, population 2 be all MS recipients from university B, and population 3 be all MS recipients from university C.) State the null and alternative hypotheses.

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