| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Wilcoxon tests |
| Type | Wilcoxon matched-pairs signed-rank test |
| Difficulty | Challenging +1.2 This is a Further Maths statistics question requiring application of the Wilcoxon signed-rank test with 7 pairs of data. While the procedure is systematic (calculate differences, rank absolute values, sum ranks, compare to critical value), it requires knowledge of a non-standard test beyond A-level core content and careful execution of multiple steps. The comparison to sign test in part (ii) requires conceptual understanding. Harder than typical A-level but routine for Further Statistics students. |
| Spec | 5.07b Sign test: and Wilcoxon signed-rank5.07c Single-sample tests |
| Elder twin | 65 | 37 | 60 | 79 | 39 | 40 | 88 |
| Younger twin | 58 | 39 | 61 | 62 | 50 | 26 | 84 |
A psychologist investigated the scores of pairs of twins on an aptitude test. Seven pairs of twins were chosen randomly, and the scores are given in the following table.
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline
Elder twin & 65 & 37 & 60 & 79 & 39 & 40 & 88 \\
\hline
Younger twin & 58 & 39 & 61 & 62 & 50 & 26 & 84 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\roman*)]
\item Carry out an appropriate Wilcoxon test at the 10\% significance level to investigate whether there is evidence of a difference in test scores between the elder and the younger of a pair of twins. [6]
\item Explain the advantage in this case of a Wilcoxon test over a sign test. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2017 Q4 [7]}}