Question

An accounting class of 250 students is allocated into several tutorials to be taken by either Tutor A and Tutor B. At the end of the semester the lecturer-in-charge looks at the distribution of marks by tutor. Table 1 provides this summary of the marks Table 1: Accounting student results according to their tutor Fail Credit Distinction Higher distinction 1 4 Pass Total Tutor A Tutor B Total 13 12 25 59 71 130 26 39 65 6 19 25 105 145 250 (i)What is the probability that a student chosen at random from the Accounting (ii)What is the probability that a student chosen at random from the Accounting (iii) Suppose a student chosen at random from the class received a credit mark. (iv) Are the events "having tutor B" and "received a distinction grade" independent (v)Suppose a formal test of the independence of tutor and grade is performed and class has Tutor B? [1 mark] class has Tutor B and received at least a passing grade? [1 mark] What is the probability that they have Tutor B? [1 mark] events? Provide a justification for your answer. [1 mark] the null hypothesis of independence is rejected at the 5% level of significance (You do not have to do this test.) Give 2 possible reasons why the test might have indicated a lack of independence for these data? [2 marks] (vi)The Head of the Accounting Department insists that all classes be graded according to a common grade distribution given by 3% Higher distinction, 12% Distinction, 25% Credit, 50% Pass and 10% Fail Test whether the actual distribution complies with this common grade distribution. Use a significance level of 1%. Be sure to state clearly your hypothesis, decision rule and conclusion. [4 marks] The Accounting Department routinely surveys graduating students and asks whether they were satisfied or not with the quality of teaching provided by the Accounting staff during their degree. In a sample of 400 graduates, 340 stated that they were satisfied. Historically the proportion of satisfied graduates has been steady at 0.8. Do the results of the recent survey provide evidence that the actual satisfaction rate has improved? Set up a formal hypothesis test stating the null and alternative hypotheses. Use a 1% significance level and perform the test making clear all assumptions that are needed to justify your calculations? [5 marks] What is a Type Il error for the test used in (vii)? Calculate the probability of a Type Il error if the population satisfaction rate is equal to 0.82. [3 marks] (vii) (viii)

Answer 1