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. Do 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.
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. Do 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.
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