Question

1. 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.

2. In the question above (California vs Arizona), if the hull hypothesis were true, what would you expect the chi-squared statistic to equal, on average?

Answer 1

1. The hypothesis being tested is:

H₀: California have the same color preferences as people in Arizona

H_a: California have not the same color preferences as people in Arizona

		Yellow	Green	Red	Total
California	Observed	35	50	15	100
	Expected	30.00	40.00	30.00	100.00
	O - E	5.00	10.00	-15.00	0.00
	(O - E)² / E	0.83	2.50	7.50	10.83
Arizona	Observed	10	10	30	50
	Expected	15.00	20.00	15.00	50.00
	O - E	-5.00	-10.00	15.00	0.00
	(O - E)² / E	1.67	5.00	15.00	21.67
Total	Observed	45	60	45	150
	Expected	45.00	60.00	45.00	150.00
	O - E	0.00	0.00	0.00	0.00
	(O - E)² / E	2.50	7.50	22.50	32.50
		5.991	critical value
		32.50	chi-square
		2	df
		8.76E-08	p-value

The test statistic is 32.50.

The critical value is 5.991.

Since 32.50 > 5.991, we can reject the null hypothesis.

Therefore, we can conclude that California have not the same color preferences as people in Arizona.

2. If the hull hypothesis were true, the chi-squared statistic would be equal to 32.50, on average.