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 46 172 791 47 173 761 49 182 800 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

H0: The proportion falling in the three credit card response categories is the same for all three years
H1: The proportion falling in the three credit card response categories is not the same for all three years
Let the los be alpha = 5%

From the given data, The observed frequencies are

	2004	2005	2006	Total
Definitely/Probably Will	46	172	791	1009
Might/Might	47	173	761	981
Definitely Not	49	182	800	1031
Total	142	527	2352	3021

The expected frequencies are

	2004	2005	2006	Total
Definitely/Probably Will	47.427	176.016	785.557	1009
Might/Might	46.111	171.131	763.758	981
Definitely Not	48.461	179.853	802.685	1031.00
Total	141.999	527	2352	3021.00

The chi-square contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
46	47.427	0.0429
172	176.016	0.0916
791	785.557	0.0377
47	46.111	0.0171
173	171.131	0.0204
761	763.758	0.01
49	48.461	0.006
182	179.853	0.0256
800	802.685	0.009
	Total:	0.2603

Degrees of freedom: 4

Test Statistic, X^2: 0.2603
Critical X^2: 9.48772
P-Value: 0.9922

Since chi-square value < Chi-square critical value and P-value > alpha 0.05 so we accept H0

Thus we conclude that the proportion falling in the three credit card response categories is the same for all three years