You and your friend Ivan are talking about the grading of your last class assignment

You and your friend Ivan are talking about the grading of your last class assignment. You glanced at the lecturer’s grade book and think that you saw the average class mark is 86. Ivan doesn’t agree because he thinks that 86 is too high to be the class average. You and Ivan decide to collect a sample of assignment marks by combining yours with those of 4 of your classmates. The sample is as follows:

88, 75, 91, 70, 68, 82

The moment Ivan sees the sample he says “Told ya! There’s no way that it’s 86. It’s just too high”. You decide to try and show him that the class average still might be 86 by constructing a hypothesis test (with significance level α = 0.05) because you claim that it’s a more powerful statistical technique. You even go so far as to promise that you’ll include:

Question:- (1) A null hypothesis and alternative hypothesis for your test;

Question:- (2) A calculation of the test statistic given the sample obtained: ?=79, =9.5 and =6

Question:- (3)  A statement of the correct distribution and corresponding critical value; and

Question:- (4)  A clear conclusion in context