Question

The number of men and women among professors in Math, Physics, Chemistry, Linguistics, and English departments from a SRS of small colleges were counted, and the results are shown in the table below.

Dept.	Math	Physics	Chemistry	Linguistics	English
Men	44	99	38	20	47
Women	9	8	6	12	29

Test the claim that the gender of a professor is independent of the department. Use the significance level α=0.01

(a) The test statistic is χ^2=

Answer 1

The following cross tablulation have been provided. The row and column total have been calculated and they are shown below:

	Column 1	Column 2	Column 3	Column 4	Column 5	Total
Row 1	44	99	38	20	47	248
Row 2	9	8	6	12	29	64
Total	53	107	44	32	76	312

Expected Values	Column 1	Column 2	Column 3	Column 4	Column 5	Total
Row 1	53*248/312 = 42.128	107*248/312 = 85.051	44*248/312 = 34.974	32*248/312 = 25.436	76*248/312 = 60.41	248
Row 2	53*64/312 = 10.872	107*64/312 = 21.949	44*64/312 = 9.026	32*64/312 = 6.564	76*64/312 = 15.59	64
Total	53	107	44	32	76	312

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0​: The gender of a professor is independent of the department

Ha​: The gender of a professor is dependent of the department

This corresponds to a Chi-Square test of independence.

Conclucion : It is concluded that the null hypothesis Ho is rejected. Therefore, there is no enough evidence to claim that the gender of a professor is independent of the department.at the 0.01 significance level.