Question

Undergraduate Degree and MBA Major (3 parts, 14 marks)

BA (=1), BEng (=2), BBA (=3), and several others (=4). There are three possible majors for the MBA students: Accounting (=1), Finance (=2), and Marketing (=3). Can the Statistics professor conclude that the undergraduate degree affects the choice of major?

1. [2 Marks] Create a cross-classified (or contingency) table with undergraduate degree as the row and MBA major as the column. The data in this table should be deemed as observed counts.
2. [3 Marks] Create another table with the corresponding expected counts and having row totals, column totals, and grand total. Round each cell value to two decimal places.
3. [9 Marks] Perform a chi-square test to assess the association (or independence) between undergraduate degree and choice of MBA major at 5% level of significance. Verify the assumptions required for the chi-square test of independence. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and show your computations.

	Degree 1	Degree 2	Degree 3	Degree 4
MBA Major 1	31	8	12	10
MBA Major 2	13	16	10	5
MBA Major 3	16	7	17	7

Answer 1

Soln

Null and Alternate Hypothesis

H₀: The two variables (MBA Major and Degree) are independent.

H_a: The two variables are associated.

a)

Observed Values:

	Degree 1	Degree 2	Degree 3	Degree 4	Total
MBA Major 1	31	8	12	10	61
MBA Major 2	13	16	10	5	44
MBA Major 3	16	7	17	7	47
Total	60	31	39	22	152

b)

Expected Values:

Expected Values are calculated as:

E_ij = (T_i * T_j)/N

where,

T_i = Total in ith row

T_j = Total in jth column

N = table grand total

	Degree 1	Degree 2	Degree 3	Degree 4
MBA Major 1	24.08	12.44	15.65	8.83
MBA Major 2	17.37	8.97	11.29	6.37
MBA Major 3	18.55	9.59	12.06	6.80

Alpha = 0.05

df = (r-1)*(c-1) = (3-1)*(4-1) = 2*3 = 6

Chi Square _Critical = 12.592

Decision Rule:

If Chi Square> Chi Square _Critical reject the null hypothesis

Test Statistic:

Chi Square = ∑(O_ij – E_ij)²/E_ij = (31-24.08)²/24.08 + ……………….. + (7 – 6.80)²/6.80 = 14.70

Result:

Since, Chi Square> Chi Square _Critical we reject the null hypothesis.

Conclusion:

MBA Major and Degree are independent.