Suppose that nationwide, the members of the Delta Tau Chi Fraternity have a grade distribution of 25% A's, 3% E's, 25% C's, 15% U5, and 5% F's among all students currently enrolled. The Dean of Students at Faher College thinks that the chapter of Delta Tau Chi fraternity at his institution may not be following this guideline, so he takes a random sample of grades to check his suspicion. A random sample of ED grades yields 9 A's, 15 E's, 3 Cs; 1 D, and 2 P's. [a] Provide the null and alternative hypotheses for the dean's test. Calculate the value of the appropriate test statistic. [b] State the critical value for this test, and your statistical decision using a 5% signicance level. Provide a concluding statement in the context ofthis situation