9231 P42 - Nov 2020 - Q2 - 9 marks
6834
A large school is holding an essay competition and each student has submitted an essay. To ensure fairness, each essay is given a mark out of 100 by two different judges. The marks awarded to the essays submitted by a random sample of 12 students are shown in the following table.
Student | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) | \(K\) | \(L\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Judge 1 | 62 | 74 | 52 | 48 | 68 | 55 | 56 | 64 | 37 | 70 | 81 | 59 |
Judge 2 | 65 | 70 | 47 | 49 | 76 | 74 | 67 | 54 | 50 | 77 | 72 | 75 |
(a) One of the students claims that Judge 2 is awarding higher marks than Judge 1.
Carry out a Wilcoxon matched-pairs signed-rank test at the \(5 \%\) significance level to test whether the data supports the student's claim.
It is discovered later that the marks awarded to student \(A\) have been entered incorrectly. In fact, Judge 1 awarded 65 marks and Judge 2 awarded 62 marks.
(b) By considering how this change affects the test statistic, explain why the conclusion of the test carried out in part (a) remains the same.
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