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

Department	Math	Physics	Chemistry	Linguistics	English
Men	43	81	30	20	29
Women	5	5	8	14	23

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

a) The test statistic is chi squared =

b) The critical value is chi squared =

c) Is there sufficient evidence to warrant the rejection of the claim that the gender of a professor is independent of the department? Yes or no?

Answer 1

Ans:

H0: the gender of a professor is independent of the department.

H_a: the gender of a professor is not independent of the department.

	Observed(fo)
Department	Math	Physics	Chemistry	Linguistics	English	Total
Men	43	81	30	20	29	203
Women	5	5	8	14	23	55
Total	48	86	38	34	52	258
	Expected(fe)
Department	Math	Physics	Chemistry	Linguistics	English	Total
Men	37.77	67.67	29.90	26.75	40.91	203
Women	10.23	18.33	8.10	7.25	11.09	55
Total	48	86	38	34	52	258
	Chi square=(fo-fe)^2/fe
Department	Math	Physics	Chemistry	Linguistics	English	Total
Men	0.725	2.627	0.000	1.704	3.470	8.526
Women	2.676	9.697	0.001	6.290	12.806	31.470
Total	3.401	12.324	0.002	7.994	16.276	39.996

a)Test statistic:

Chi square=39.996

b)df=(2-1)*(5-1)=4

critical chi square value=CHIINV(0.025,4)=11.143

c)As,test statistic is greater than critical chi square,we reject the null hypothesis.

Yes,there is sufficient evidence to warrant the rejection of the claim that the gender of a professor is independent of the department.