5. The test score of 5 students in subject A in a class is Student Marks out of 100 60 2 45 55 4 85 35 Assume the marks of students is i.i.d. and the distribution is normal. a) Construct the 90% confidence interval for the average marks of the class in subject A. b) Test the hypothesis that the average mark of the class is 50 in subject A. Compute the bound for the p-value using the appropriate distribution table. c) The performance in subject B is Student Marks out of 100 80 2 25 60 4 90 60 Test the hypothesis that subject A is more difficult than subject B at significance level 0.1. [Hint: It is to test whether it is more difficult, not whether the tests are different. Also, the same 5 students are taking test A and test B. Make sure that you use the correct test in this question.]