Question

Victoria is doing a chi-square test to see if people in California have the same color preferences as people in Arizona. 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 Arizonans 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 Victoria should conclude about Californian’s and Arizonan’s color preferences? Let α = .05.

if the hull hypothesis were true, what would you expect the chi-squared statistic to equal, on average?

Answer 1

Observed Frequencies:

	Yellow	Green	Red	Totals
Californian	35=O11	50=O12	15=O13	100=O10
Arizonan	10=O21	10=O22	30=O23	50=O20
Totals	45=O01	60=O02	45=O03	150=N

Expected Frequencies:

	Yellow	Green	Red
Californian	30	40	30
Arizonan	15	20	15

	Yellow	Green	Red
Californian	0.8333	2.5	7.5
Arizonan	1.6667	5	15

There is insufficient evidence to conclude that the people in California have the same color preferences as people in Arizona.

If the null hypothesis were true, the chi-squared statistic=0 (since under null hypothesis, O_ij=E_ij for all i=1,2, j=1,2,3).