Question

QUES The number of students admitted to the three largest graduate programs at Indiana University are given in the table below. We wish to test whether department and sex are independent. The data are shown in the table below. Department Men admitted Women admitted A 512 B 353 с 120 202 89 17 a. Calculate the chi-square test statistic for a test of independence on this data. Please round the nearest integer. Please type either A or B. b. Using either classical approach or P-value approach, we will conclude: A There is sufficient evidence to conclude that department and sex are associated. B. There is insufficient evidence to conclude that department and sex are associated.

Answer 1

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Men	Women	Total
	A	457.8384	143.1616	601
	B	281.8639	88.1361	370
	C	245.2978	76.7022	322
	total	985	308	1293
chi square    χ2	=(Oi-Ei)2/Ei	Men	Women	Total
	A	6.407	20.491	26.8980
	B	17.953	57.415	75.3683
	C	64.002	204.681	268.6834
	total	88.3623	282.5873	370.9496
test statistic X2=		371

b)

correct option is A

A. There is sufficient evidence to conclude that department and sex are associated.