Solve the below:
Q: The director of admissions has had questions from potential freshmen regarding the average price of textbooks per semester. In order to make an informed estimate of this cost, he selected a sample of 100 students and recorded their text book expenses for the most recent semester. He found a sample mean of $391.52. He assumes that the standard deviation of semester costs here is the same as the national (at $43.70).
a. What should he report as the average cost, if he wants to be 80% confident of his answer?
b. Is the sample mean here the same as the nationally reported average of $401.86? Use a 20% level of significance.