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 $3,779. The bank randomly selected 23 credit-card holders and determined the amounts they charged. For this sample group, the mean is $3,612 and the standard deviation is $331. 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 $3,779. Based on the result, will a reward program be implemented?

(a) State the null and alternative hypotheses, and identify which one is the claim.