Question

(3 points) 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 46 91 39 17 37 Women 10 9 8 15 20 Test the claim that the gender of a professor is independent of the department. Use the significance level a = 0.01 (a) The test statistic is x2 = (b) The critical value is x2 = (c) Is there sufficient evidence to warrant the rejection of the claim that the gender of a professor is independent of the department? A. No B. Yes

Answer 1

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Math	Physics	chemistry	Linguistics	English	Total
	male	44.11	78.77	37.02	25.21	44.90	230
	female	11.89	21.23	9.98	6.79	12.10	62
	total	56	100	47	32	57	292
chi square    χ2	=(Oi-Ei)2/Ei	Math	Physics	chemistry	Linguistics	English	Total
	male	0.0810	1.8998	0.1058	2.6712	1.3891	6.1470
	female	0.3005	7.0477	0.3926	9.9094	5.1531	22.8034
	total	0.3816	8.9475	0.4985	12.5807	6.5422	28.9505
test statistic X2 =		28.9505

B)

for 4 df and 0.01 level , critical value       χ2=

13.2767

C()

Yes