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A major bank is interested about the amount of debt being accrued by customers using its credit cards. The Board of Directors voted to institute a reward program if the mean for all of the bank's customers is less than $2,748. The bank randomly selected 29 credit-card holders and determined the amounts they charged. For this sample group, the mean is $2,590 and the standard deviation is $429. It is assumed that the distribution of amounts of debt in the population of all bank customers is symmetric and bell-shaped, i.e. approximately normal. Use a 0.02 level of significance to test the claim that the mean amount charged is less than $2,748. Based on the result, will a reward program be implemented? Round to 3 decimal places where appropriate. (a) State the null and alternative hypotheses, and identify which one is the claim. Ho_@:] H._@:] Which one is the claim: H1 H0 For parts (b), (c) use the correct sign for the t-value and test statlstic. {b} What is the critical t-value? :] {c} What is the test statistic? :} (d) Is the null hypothesis rejected? YES No (e) Is the claim supported? No, there is not sufficient evidence to institute a reward program. Yes, there is sufficient evidence to institute a reward program