Question

Test the null hypothesis of independence of the two classifications A and B of the 3x2 contingency table shown below. Use alpha = 0.05.

	Males	Females
In Favor of X	40	72
Against X	63	53

where X can be any policy issue. The null hypothesis is that gender (Males/Females) does not affect the views on X (in favor/against). The alternative is that there is a gender bias ( the view is not independent of gender) . Remember that the problem has a test statistic that follows the chi-square distribution.

Answer 1

null hypothesis : gender and view on X are independent

Alternate hypothesis : gender and view on X are not independent

degree of freedom(df) =(rows-1)*(columns-1)=		1
for 1 df and 0.05 level , critical value       χ2=		3.841
Decision rule : reject Ho if value of test statistic X2>3.841

Applying chi square test of independence:

Observed		males	females	Total
	in favor	40	72	112
	against	63	53	116
	total	103	125	228
Expected	Ei=row total*column total/grand total	males	females	Total
	in favor	50.596	61.404	112.00
	against	52.404	63.596	116.00
	total	103.00	125.00	228.00
chi square    χ2	=(Oi-Ei)2/Ei	males	females	Total
	in favor	2.219	1.829	4.0479
	against	2.143	1.7656	3.9083
	total	4.3619	3.5942	7.956
test statistic X2 =		7.956

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that gender and view on X are not independent