The polling organization Ipsos conducted telephone surveys in March of 2004, 200

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.)

2 =  
P-value interval

p < 0.001

0.001 p < 0.01    

0.01 p < 0.05

0.05 p < 0.10

p 0.10

Conclusion

The proportion falling in the three credit card response categories is the same for all three years.

The proportion falling in the three credit card response categories is not the same for all three years.

Intent to Pay Taxes with a Credit Card    2004 2005 2006 Definitely/Probably Will
Might/Might Not/Probably Not
Definitely Not 42
181
790 40
175
792 43
170
782

Explanation / Answer

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.

The expected frequencies are

The chisquare test statistic is calculated as

Test Statistic, X^2: 0.3623

Critical X^2: 9.48772
P-Value: 0.9854

Correct answer: (E) p 0.10

Here P value > alpha, we accept H0

Thus we conclude that

The proportion falling in the three credit card response categories is the same for all three years.

2004 2005 2006 Total Definitely 41.998 41.75 41.252 125 Probably No 176.729 175.682 173.589 526 Definitely Not 794.273 789.568 780.159 2364 Total 1013 1007 995 3015

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