A credit card company claims that the mean credit card debt for individuals is greater than $5,000. You want to test this claim. You find that a random sample of 33 cardholders has a mean credit card balance of $5,196 and a standard deviation of $625. At a = 0.01, can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Write the claim mathematically and identify Ho and Ha. Which of the following correctly states Ho and H,? O A. Ho: us $5,000 Ha:u> $5,000 O B. Ho: H2 $5,000 Ha: H < $5,000 O C. Ho: u> $5,000 Hai us $5,000 O D. Ho: H = $5,000 O E. Ho: u = $5,000 O F. Ho: u> $5,000 Ha:us $5,000 Ha: u > $5,000 Ha: u# $5,000 (b) Find the critical value(s) and identify the rejection region(s). What is(are) the critical value(s), to? to =O (Use a comma to separate answers as needed. Round to three decimal places as needed.) Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.) O A. t < . O D. t < and t> (c) Find the standardized test statistic t. |(Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. A. Reject Ho because the test statistic is not in the rejection region. B. Reject Ho because the test statistic is in the rejection region. O C. Fail to reject H, because the test statistic is in the rejection region. O D. Fail to reject H, because the test statistic is not in the rejection region. (e) Interpret the decision in the context of the original claim. O A. At the 1% level of significance, there is not sufficient evidence to support the claim that the mean credit card debt is less than $5,000. O B. At the 1% level of significance, there is sufficient evidence to support the claim that the mean credit card debt is greater than $5,000. O C. At the 1% level of significance, there is not sufficient evidence to support the claim that the mean credit card debt is greater than $5,000. O D. At the 1% level of significance, there is sufficient evidence to support the claim that the mean credit card debt is less than $5,000.