Question 1

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 an expensive monitoring system if the mean for all of the bank's customers is greater than $2,052. The bank randomly selected 32 credit-card holders and determined the amounts they charged. For this sample group, the mean is $2,346 and the standard deviation is $720. 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 0.01 level of significance to test the claim that the mean amount charged is greater than $2,052. Based on the result, will an expensive monitoring system be implemented? Round to 3 decimal places where appropriate. (a) State the null and alternative hypotheses, and identify which one is the claim. H0: seleCt an anSwer a ? [: Which one is the claim: ,\\ H0 _\\ H1 For parts (b), (c) use the correct sign for the t-value and test statistic. (b) What is the critical t-value? :] (c) What is the test statistic? [: (d) Is the null hypothesis rejected? 7' No \" Yes