9231 P41 - Nov 2024 - Q2 - 9 marks
6840
A school with a large number of students is updating its logo. Each student has designed a new logo and two teachers have each awarded a mark out of 50 for each logo. The marks awarded to a random sample of 12 students are shown in the following table.
Student | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) | \(K\) | \(L\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Teacher 1 | 36 | 38 | 40 | 36 | 22 | 34 | 45 | 44 | 48 | 35 | 28 | 30 |
Teacher 2 | 38 | 42 | 32 | 41 | 32 | 41 | 42 | 50 | 36 | 44 | 42 | 41 |
One of the students claims that Teacher 2 is awarding higher marks than Teacher 1.
(a) Carry out a Wilcoxon matched-pairs signed-rank test, at the \(5 \%\) significance level, to test whether the data supports the claim.
It was later discovered that Teacher 1 had entered her mark for student \(C\) incorrectly. Her intended mark was 24 not 40 . This was corrected.
(b) Determine whether this correction affects the conclusion of the test carried out in part (a).
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