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 Pass Credit Distinction Higher distinction Total Tutor A 13 59 26 6 1 105 Tutor B 12 71 39 19 4 145 Total 25 130 65 25 5 250 (i) What is the probability that a student chosen at random from the Accounting class has Tutor B? [1 mark] (ii) What is the probability that a student chosen at random from the Accounting class has Tutor B and received at least a passing grade? [1 mark] (iii) Suppose a student chosen at random from the class received a credit mark. What is the probability that they have Tutor B? [1 mark] (iv) Are the events "having tutor B" and "received a distinction grade" independent events? Provide a justification for your answer. [1 mark] (v) Suppose a formal test of the independence of tutor and grade is performed and 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] (vii) 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] (viii) What is a Type II error for the test used in (vii)? Calculate the probability of a Type II error if the population satisfaction rate is equal to 0.82. [3 marks]

          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 Pass Credit Distinction Higher distinction Total
Tutor A 13 59 26 6 1 105
Tutor B 12 71 39 19 4 145
Total 25 130 65 25 5 250

(i) What is the probability that a student chosen at random from the Accounting class has Tutor B? [1 mark]
(ii) What is the probability that a student chosen at random from the Accounting class has Tutor B and received at least a passing grade? [1 mark]
(iii) Suppose a student chosen at random from the class received a credit mark. What is the probability that they have Tutor B? [1 mark]
(iv) Are the events "having tutor B" and "received a distinction grade" independent events? Provide a justification for your answer. [1 mark]
(v) Suppose a formal test of the independence of tutor and grade is performed and 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]
(vii) 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]
(viii) What is a Type II error for the test used in (vii)? Calculate the probability of a Type II error if the population satisfaction rate is equal to 0.82. [3 marks]

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 Pass Credit Distinction Higher distinction Total
Tutor A 13 59 26 6 1 105
Tutor B 12 71 39 19 4 145
Total 25 130 65 25 5 250

(i) What is the probability that a student chosen at random from the Accounting class has Tutor B? [1 mark]
(ii) What is the probability that a student chosen at random from the Accounting class has Tutor B and received at least a passing grade? [1 mark]
(iii) Suppose a student chosen at random from the class received a credit mark. What is the probability that they have Tutor B? [1 mark]
(iv) Are the events "having tutor B" and "received a distinction grade" independent events? Provide a justification for your answer. [1 mark]
(v) Suppose a formal test of the independence of tutor and grade is performed and 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]
(vii) 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]
(viii) What is a Type II error for the test used in (vii)? Calculate the probability of a Type II error if the population satisfaction rate is equal to 0.82. [3 marks]

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