| Exam Board | OCR |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2018 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Wilcoxon rank-sum test (Mann-Whitney U test) |
| Difficulty | Standard +0.3 This is a straightforward application of the Wilcoxon rank-sum test with small sample sizes (n=8, m=5). Students must rank the combined data, sum ranks for one group, and compare to critical values from tables. While it requires careful ranking and arithmetic, it's a standard bookwork procedure with no conceptual challenges or novel problem-solving—slightly easier than average since it's purely mechanical application of a learned technique. |
| Spec | 5.07d Paired vs two-sample: selection |
| Men | 4 | 7 | 10 | 13 | 16 | 17 | 20 | 21 |
| Women | 1 | 2 | 14 | 18 | 22 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(H_0\): (popn median distances equal) \(H_1\): (popn median distances not equal) | B1 | |
| Ranks 3 4 5 6 8 9 11 12 / 1 2 7 10 13 | B1 | Can be implied by correct later working |
| \(R_m = 33\), \(m(n+m+1) - R_m = 37\) | B1B1 | |
| \(W = 33\) | B1 | |
| \(CV = 21\) | B1 | |
| \(33 > 21\), do not reject \(H_0\) | M1 | ft TS and CV |
| Insufficient evidence that the (popn) median distances are different | A1, [8] | CWO, contextualised, not over-assertive |
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $H_0$: (popn median distances equal) $H_1$: (popn median distances not equal) | B1 | |
| Ranks 3 4 5 6 8 9 11 12 / 1 2 7 10 13 | B1 | Can be implied by correct later working |
| $R_m = 33$, $m(n+m+1) - R_m = 37$ | B1B1 | |
| $W = 33$ | B1 | |
| $CV = 21$ | B1 | |
| $33 > 21$, do not reject $H_0$ | M1 | ft TS and CV |
| Insufficient evidence that the (popn) median distances are different | A1, [8] | CWO, contextualised, not over-assertive |
---2 The distances from home to work, in km , of 8 men and 5 women were recorded and are given below. The workers were chosen at random.
\begin{center}
\begin{tabular}{ l c c c c c c c c }
Men & 4 & 7 & 10 & 13 & 16 & 17 & 20 & 21 \\
Women & 1 & 2 & 14 & 18 & 22 & & & \\
\end{tabular}
\end{center}
Carry out a Wilcoxon rank-sum test at the $5 \%$ significance level to test whether there is a significant difference between the distances from home to work between men and women.
\hfill \mbox{\textit{OCR S4 2018 Q2 [8]}}