9231 P43 - Jun 2024 - Q1 - 7 marks
6667
A college uses two assessments, \(X\) and \(Y\), when interviewing applicants for research posts at the college. These assessments have been used for a large number of applicants this year.
The scores for a random sample of 9 applicants who took assessment \(X\) are as follows.
| 21.4 | 24.6 | 25.3 | 22.7 | 20.8 | 21.5 | 22.9 | 21.3 | 22.3 |
The scores for a random sample of 10 applicants who took assessment \(Y\) are as follows.
| 20.9 | 23.5 | 24.8 | 21.9 | 23.4 | 24.0 | 23.8 | 24.1 | 25.1 | 25.8 |
The interviewer believes that the population median score from assessment \(X\) is lower than the population median score from assessment \(Y\).
Carry out a Wilcoxon rank-sum test, at the \(1 \%\) significance level, to test whether the interviewer's belief is supported by the data.
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