Question

The polling organization Ipsos conducted telephone surveys in March of 2004, 2005 and 2006. In each year, 1001 people age 18 or older were asked about whether they planned to use a credit card to pay federal income taxes that year. The data are given in the accompanying table. Is there evidence that the proportion falling in the three credit card response categories is not the same for all three years? Test the relevant hypotheses using a .05 significance level. (Use 2 decimal places.)

Intent to Pay Taxes with a Credit Card
	2004	2005	2006
Definitely/Probably Will Might/Might Not/Probably Not Definitely Not	45 175 761	43 169 798	43 168 767

χ² =  
P-value interval

p < 0.001

0.001 ≤ p < 0.01    

0.01 ≤ p < 0.05

0.05 ≤ p < 0.10

p ≥ 0.10

Answer 1

		c1	c2	c3	sum
	r1	45	43	43	131
	r2	175	169	168	512
	r3	761	798	767	2326
	sum	981	1010	978	2969
	Eij	1	2	3
expected	1	43.28427	44.56383	43.1519
	2	169.1721	174.1731	168.6548
	3	768.5436	791.2631	766.1933
	Oi	45	43	43	175	169	168	761	798	767
	Ei	43.28	44.56	43.15	169.17	174.17	168.65	768.54	791.26	766.19
	(Oi-Ei)^2/Ei	0.068	0.055	0.001	0.201	0.154	0.003	0.074	0.057	0.001
	sum	0.613
	critical value	9.487729
	p-value	0.9616

TS = 0.61

p-value = 0.9616

hence

p >= 0.10

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