9231 P44 - Jun 2025 - Q2 - 7 marks
6852
The level of sound produced by a particular type of machine was measured for a random sample of 11 such machines. The results, in suitable units, are shown below.
| Machine | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) | \(K\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Sound level | 7.66 | 8.48 | 8.21 | 7.98 | 8.01 | 7.77 | 8.25 | 8.11 | 8.03 | 8.16 | 7.92 |
(a) Use a Wilcoxon signed-rank test to test whether the average sound level produced by this type of machine is more than 8.00. Use a \(5 \%\) significance level.
(b) Give a reason why a Wilcoxon signed-rank test may be more appropriate than a \(t\)-test in this case.
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