Each person in a representative sample of 449 college students age 18 to 24 was classified according to age and to the response to the following question: "How often have you used a credit card to buy...

Extracted text: Each person in a representative sample of 449 college students age 18 to 24 was classified according to age and to the response to the following question: "How often have you used a credit card to buy items knowing you wouldn't have money to pay the bill when it arrived?" Possible responses were never, rarely, sometimes, or frequently. The responses are summarized in the table. Age 18 to 20 Age 21 to 22 Age 23 to 24 Never 73 62 29 Rarely 38 34 32 Sometimes 30 42 40 Frequently 13 24 A USE SALT Do these data provide evidence that there is an association between age group and the response to the question? Test the relevant hypotheses using a = 0.01. State the appropriate null and alternative hypotheses. O H: The proportions falling into each of the three age groups are not the same for all four responses to the question. H: The proportions falling into each of the three age groups are the same for all four responses to the question. O Hg: The proportions falling into each of the three age groups are the same for all four responses to the question. H: The proportions falling into each of the three age groups are not the same for all four responses to the question. O Hg: There is no association between age group and the response to the question. H: There is an association between age group and the response to the question. O H: There is an association between age group and the response to the question. H: There is no association between age group and the response to the question. Calculate the test statistic. (Round your answer to two decimal places.) x* = Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value = State the conclusion in the problem context. O Fail to reject H. There is not convincing evidence that there is an association between age group and the response to the question. O Reject Hg. There is convincing evidence that there is an association between age group and the response to the question. O Fail to reject H. There is convincing evidence that there is an association between age group and the response to the question. O Reject Hg. There is not convincing evidence that there is an association between age group and the response to the question.