Question

Janna is doing a chi-square test to see if people in California have the same color preferences as people in Nevada. A sample of 100 Californians were polled. Thirty-five people prefer yellow, fifty people prefer green, and fifteen people prefer red. A sample of 50 people from Nevada were polled. Ten people prefer yellow, ten people prefer green, and thirty people prefer red. Calculate the test statistic. State the critical value. Come to a conclusion about the null hypothesis. And state what Janna should conclude about people from California and people from Nevada's color preferences? Let α = .05.

Answer 1

a)

Null hypothesis: Ho: Color preference and region are independent

Alternate hypothesis: Ha: Color preference and region are dependent

degree of freedom(df) =(rows-1)*(columns-1)=		2
for 2 df and 0.05 level,critical value χ2=		5.991
Decision rule : reject Ho if value of test statistic X2>5.991

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Yellow	Green	Red	Total
	California	30.0	40.0	30.0	100
	Nevada	15.0	20.0	15.0	50
	total	45	60	45	150
chi square    χ2	=(Oi-Ei)2/Ei	Yellow	Green	Red	Total
	California	0.833	2.500	7.500	10.8333
	Nevada	1.667	5.000	15.000	21.6667
	total	2.5000	7.5000	22.5000	32.5000
test statistic X2=		32.500

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that Color preference and region are dependent