Question

(1 point) 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 40 93 41 26 36 Women 9 10 10 13 27 Test the claim that the gender of a professor is independent of the department. Use the significance level α-001 (a) The test statistic isz2 (b) The critical value is χ (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 OB. Yes Note: You can earn partial credit on this problem.

Answer 1

Ho: gender and department are indepedent

H1: gender and department are not independent

Chi-Square Test
Observed Frequencies
	Column variable							Calculations
Row variable	math	physics	chemistry	linguistics	english	Total		fo-fe
men	40	93	41	26	36	236		2.085246	13.30164	1.537705	-4.17705	-12.7475
women	9	10	10	13	27	69		-2.08525	-13.3016	-1.5377	4.177049	12.74754
Total	49	103	51	39	63	305
Expected Frequencies
	Column variable
Row variable	math	physics	chemistry	linguistics	english	Total		(fo-fe)^2/fe
men	37.91475	79.69836	39.4623	30.17705	48.74754	236		0.114685	2.220041	0.059919	0.578179	3.333497
women	11.08525	23.30164	11.5377	8.822951	14.25246	69		0.392256	7.593183	0.20494	1.97754	11.40153
Total	49	103	51	39	63	305

a)

chi square test stat =Σ(fo-fe)^2/fe =27.876

b)

Df=(r-1)(c-1) =(2-1)(5-1)=4

α=0.01

critical value = 13.277 [excel fucntion:   =CHISQ.INV.RT(0.01,4) ]

c)

chi square stat > critical value , reject Ho

so, answer is yes