Suppose a population of students in a large class takes an exam and the grades (out of 100) are approximately distributed N(mu,9) . The instructor places the prior mu approximately N(65,1) on the unknown parameter. A sample of 10 grades is given below:

46, 68, 34, 86, 75, 56, 77, 73, 53, 64

a) Determine the posterior mode and a 0.95 credible interval for mu. What does this interval tell you about the accuracy of the estimate?

b) Use the 0.95 credible interval for mu to test the hypothesis H₀ : mu = 65