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	77	102	47	28	50
Women	5	6	10	13	30

Test the claim that the gender of a professor is independent of the department. Use the significance level α=0.025

(a) The test statistic is χ2=

Answer 1

	Column 1	Column 2	Column 3	Column 4	Column 5	Total
Row 1	77	102	47	28	50	304
Row 2	5	6	10	13	30	64
Total	82	108	57	41	80	368

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.

Conclusion

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 significance level α =0.025