1 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. $$\begin{array} { l l l l l l l l l } 21.4 & 24.6 & 25.3 & 22.7 & 20.8 & 21.5 & 22.9 & 21.3 & 22.3 \end{array}$$ The scores for a random sample of 10 applicants who took assessment \(Y\) are as follows. $$\begin{array} { l l l l l l l l l l } 20.9 & 23.5 & 24.8 & 21.9 & 23.4 & 24.0 & 23.8 & 24.1 & 25.1 & 25.8 \end{array}$$ 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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