Question

Classwork 12.2 Test for Independence and Homogeneity of Proportion 1. The contingency table below shows the results of a random sample of 200 registered voters that was conducted to see whether their opinions on a bill are related to their party affiliation. Test the claim of independence. Party Opinion Approve Disapprove No Opinion 42 Republican Democrat Independent 50

Answer 1

Null hypothesis: Ho :Opinion and Party Affiliation are independent

Alternate hypothesis: Ha :Opinion and Party Affiliation are dependent

degree of freedom(df) =(rows-1)*(columns-1)=		4
for 4 df and 0.05 level of signifcance critical region       χ2=			9.488
Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Approve	Disapprove	No opinion	Total
	Republican	38.7600	22.8000	14.4400	76
	Democrat	46.9200	27.6000	17.4800	92
	Independent	16.3200	9.6000	6.0800	32
	total	102	60	38	200
chi square    χ2	=(Oi-Ei)2/Ei	Approve	Disapprove	No opinion	Total
	Republican	0.2708	0.3439	0.0134	0.6281
	Democrat	0.2022	0.4696	0.0155	0.6872
	Independent	2.4475	4.2667	0.0011	6.7152
	total	2.9205	5.0801	0.0299	8.0305
test statistic X2 =		8.0305

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that :Opinion and Party Affiliation are dependent at 0.05 level of significance