9231 P41 - Jun 2021 - Q5 - 8 marks
6795
Georgio has designed two new uniforms \(X\) and \(Y\) for the employees of an airline company. A random sample of 11 employees are each asked to assess each of the two uniforms for practicality and appearance, and to give a total score out of 100. The scores are given in the table.
| Employee | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) | \(K\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Uniform \(X\) | 82 | 74 | 42 | 59 | 60 | 73 | 94 | 98 | 62 | 36 | 50 |
| Uniform \(Y\) | 78 | 75 | 63 | 56 | 67 | 82 | 99 | 90 | 72 | 48 | 61 |
(a) Give a reason why a Wilcoxon signed-rank test may be more appropriate than a \(t\)-test for investigating whether there is any evidence of a preference for one of the uniforms.
(b) Carry out a Wilcoxon matched-pairs signed-rank test at the \(10\%\) significance level.
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