| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 9 |
| Topic | Wilcoxon tests |
| Type | Wilcoxon rank-sum test (Mann-Whitney U test) |
| Difficulty | Standard +0.8 This is a Mann-Whitney U test (Wilcoxon rank-sum) question from Further Statistics requiring knowledge of a non-standard distribution-free test, calculation of test statistic from rank sums, use of tables, and understanding of assumptions. While methodical, it's beyond standard A-level and requires familiarity with a specialized technique not in core A-level, placing it moderately above average difficulty. |
| Spec | 5.07d Paired vs two-sample: selection |
Jo can use either of two different routes, A or B, for her journey to school. She believes that route A has shorter journey times. She measures how long her journey takes for 17 journeys by route A and 12 journeys by route B. She ranks the 29 journeys in increasing order of time taken, and she finds that the sum of the ranks of the journeys by route B is 219.
\begin{enumerate}[label=(\alph*)]
\item Test at the 10\% significance level whether route A has shorter journey times than route B. [8]
\item State an assumption about the 29 journeys which is necessary for the conclusion of the test to be valid. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2021 Q1 [9]}}