Help: In a given year, the average student loan of students graduating from universities in the US was $38000. a. That year 1500 graduating students from one state were selected at random and their student loans were recorded. The average student loan for these 1500 students was found to be $35000 with a standard deviation of $5000. Does the evidence imply that the average student loan in this state was less than the national average? Explain. b. If one is interested in a 99% confidence interval for the mean, with a desired margin of error is $1000, what is the minimum sample size needed for such an analysis? Was the sample size in (a) adequate? c. What is the probability of Type Il error for the test in part a. if the probability of Type I error is 5% and the specific alternative is $37000