professor claims that 50% of his students in a large class achieve a final score of 90 points or higher

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1 (15%) (2016 Test) A professor claims that 50% of his students in a large class achieve a final score of 90 points or higher. A suspicious student asks 17 randomly selected students from the professor’s class and they report. the following Scores.

80 81 87 94 79 78 89 90 92 88 81 79 82 79 77 89 90

Do the (tata suggest that the professor’s claim is not consistent with the evidence, i.e., that the mne(hian is not equal to 90? Perform the binomial test at the 5% significance level an(L also obtain the exact p—value of tile test. 

2. (25%) (2016 Exam) A statistics course has two tutorial classes con(Iucte(1 1w two tutors,Amy and Emily. Students of this course were given a 1111(1—tenu test an(L SOH1C stu(lents were randomly drawui from each of two tutorial classes and their test scores are shown below:

Anìv’s class 82 74 87 86 75

Emily’s class 88 77 91 88 94 93 83 91

Ve are testing the null hypothesis that there is no difference in statistics ability, as flÌea.SUre(l by t his test, iii tite two classes.

(a) State your tutu and alternative livpothese.s with appropriate notation.

(b) Carry out Mann—Vliit ne test and state our conclusion vitlì 5% significance level by using tite critical value approach.

(c) Someone commented that Rejccting the ¡mli hypothesis implies that one of the tutors should perforuti better.”. Do voit agree? Give a reason to support your argunielit.

(d) Denote F(x) an(l FE(x) as the cumulative distribution functions of a test score x received by a stu(ldnt in Amy’s class and Emily’s class, respectively. F’ind an approximate 90%

confidence interval for F4(85) — FE(85).

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