5 A company is deciding which of two machines, \(X\) and \(Y\), can make a certain type of electrical component more quickly. The times taken, in minutes, to make one component of this type are recorded for a random sample of 8 components made by machine \(X\) and a random sample of 9 components made by machine \(Y\). These times are as follows.
| Machine \(X\) | 4.0 | 4.6 | 4.7 | 4.8 | 5.0 | 5.2 | 5.6 | 5.8 | |
| Machine \(Y\) | 4.5 | 4.9 | 5.1 | 5.3 | 5.4 | 5.7 | 5.9 | 6.3 | 6.4 |
The manager claims that on average the time taken by machine \(X\) to make one component is less than that taken by machine \(Y\).
- Carry out a Wilcoxon rank-sum test at the \(5 \%\) significance level to test whether the manager's claim is supported by the data.
- Assuming that the times taken to produce the components by the two machines are normally distributed with equal variances, carry out a \(t\)-test at the \(5 \%\) significance level to test whether the manager's claim is supported by the data.
\section*{Question 5(c) is printed on the next page.} - In general, would you expect the conclusions from the tests in parts (a) and (b) to be the same? Give a reason for your answer.
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