Question

Use a χ2 test to test the claim that in the given contingency table, the row variable and the column variable are independent. Responses to a survey question are broken down according to gender and the sample results are given below. At the 0.05 significance level, test the claim that response and gender are independent.

male: 25, 50,15

female: 20,30,10

test statistic

critical value

accept or reject

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	x1	x2	x3	Total
	male	27.0000	48.0000	15.0000	90.00
	female	18.0000	32.0000	10.0000	60.00
	total	45.00	80.00	25.00	150.00
chi square    χ2	=(Oi-Ei)2/Ei	x1	x2	x3	Total
	male	0.148	0.083	0.000	0.2315
	female	0.222	0.125	0.000	0.3472
	total	0.3704	0.2083	0.0000	0.579
test statistic X2 =		0.5787

for 2 df and 0.05 level , critical value       χ2=

5.991

since test statistic <critical value

accept