In one statistics class, students were given one homework assignment. The professor asked students to find an example of a multinomial population and then to develop a hypothesis test. One student found an example - He selected four classes in fall 2010: Management, Accounting, Finance, and Economics. He computed the proportion of students who received an A grade for each class in fall 2010. The proportion of students who received an A grade in Management (M), Accounting (A), Finance (F), and Economics (E) is 0.45, 0.25, 0.3, and 0.2, respectively. In fall 2011, a new hired Economics professor teaches Economics. The student wants to study whether or not the new Economics professor will affect the proportion of students who will receive an A grade in these four classes in fall 2011. The enrollments of these four classes are 54, 48, 52, and 64, respectively. Therefore, this student formulates the null hypothesis: P(M) = 0.45, P(A) = 0.25, P(F) = 0.3, and P(E) = 0.2; while the alternative hypothesis is: The population proportion are not P(M) = 0.45, P(A) = 0.25, P(F) = 0.3, and P(E) = 0.2. Does this student's example and hypothesis test make any sense? If yes, explain why you think so; if no, explain why not. Discuss and explain your reasons. You must provide your statistical analysis and reasons.