Question

A U.S.-based Internet company offers an online proficiency course in basic accounting. Completing this online course satisfies the Fundamentals of Accounting course requirement in many MBA programs. In the first semester, 315 students have enrolled in the course. The marketing research manager divided the country into seven regions of approximately equal population. The course enrollment values for each of the seven regions are given below. The management wants to know if there is equal interest in the course across all regions. (Region) Enrollment (1) 45 (2) 60 (3) 30 (4) 40 (5) 50 (6) 55 (7) 35. At a significance level of .05, test H0: the probabilities are equal for all seven regions. Discuss.

Answer 1

Null Hypothesis H0: the probabilities are equal for all seven regions

Alternative Hypothesis H1: The probabilities are not equal for all seven regions.

Under H0, the expected probabilities are :

E = (45+60+30+40+50+55+35)/7 =45

The calculations for chi square is

Region	Enrollment (obs. Freq) O	Exp. Freq ( E )	(O-E)^2/E
1	45	45	0.000
2	60	45	5.000
3	30	45	5.000
4	40	45	0.556
5	50	45	0.556
6	55	45	2.222
7	35	45	2.222
Total	315	315	15.556

The test statistic is

Degrees of freedom = n-1 = 6

Significance Level

The critical value of chi square for 6 df at 5% significance level is 12.592

Since chi square calculated is greater than chi square tabulated, Reject H0.

Hence, the probabilities are not equal for all seven regions.