Question: It has been reported that the mean credit card debt for college seniors at the college bookstore for a specific college is $3262. The student senate at a large university feels that their seniors have a debt much less than this. The student senate conducts a study of 50 randomly selected seniors and finds their average debt is \(\bar{X}=\\)2995$ with a population standard deviation \(\sigma =\\)1100$. Using \(\alpha =0.05\), test the claim that the student senate is correct in saying their seniors have a lower debt than $3262. Decide whether the normal distribution or the t-distribution should be used. Report the p-value for the test.