CAIE Further Paper 4 2021 June — Question 5

Exam BoardCAIE
ModuleFurther Paper 4 (Further Paper 4)
Year2021
SessionJune
TopicWilcoxon tests

5 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 \(X\)8274425960739498623650
Uniform \(Y\)7875635667829990724861
  1. 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.
  2. Carry out a Wilcoxon matched-pairs signed-rank test at the \(10 \%\) significance level.