| Exam Board | OCR |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2016 |
| 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 clear data, standard hypotheses, and a routine procedure (rank all values, sum ranks for one group, compare to critical value). The context is accessible and the test is mechanical once learned, making it slightly easier than average for an S4 question. |
| Spec | 5.07a Non-parametric tests: when to use5.07d Paired vs two-sample: selection |
| Treatment \(A\) | 189 | 168 | 176 | 186 | 183 | 187 | 188 | |
| Treatment \(B\) | 177 | 179 | 173 | 180 | 178 | 170 | 175 | 174 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(H_0: m_A = m_B\), \(H_1: m_B < m_A\) | B1 | For both. Allow any sensible hypotheses |
| Attempt ranks | M1 | |
| 15, 1, 6, 12, 11, 13, 14; 7, 9, 3, 10, 8, 2, 5, 4 | A1 | |
| \(R_m = 72\) | A1 | |
| \(W = 40\) | A1 | |
| \(CV = 41\) | B1 | |
| "40" \(< 41\) reject \(H_0\) | M1 | Ft TS and CV |
| Evidence that treatment \(B\) is more effective | A1 | In context, not over-assertive. Cwo |
| [8] |
# Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $H_0: m_A = m_B$, $H_1: m_B < m_A$ | B1 | For both. Allow any sensible hypotheses |
| Attempt ranks | M1 | |
| 15, 1, 6, 12, 11, 13, 14; 7, 9, 3, 10, 8, 2, 5, 4 | A1 | |
| $R_m = 72$ | A1 | |
| $W = 40$ | A1 | |
| $CV = 41$ | B1 | |
| "40" $< 41$ reject $H_0$ | M1 | Ft TS and CV |
| Evidence that treatment $B$ is more effective | A1 | In context, not over-assertive. Cwo |
| **[8]** | | |
---2 Low density lipoprotein (LDL) cholesterol is known as 'bad' cholesterol.\\
15 randomly chosen patients, each with an LDL level of 190 mg per decilitre of blood, were given one of two treatments, chosen at random. After twelve weeks their LDL levels, in mg per decilitre, were as follows.
\begin{center}
\begin{tabular}{ l l l l l l l l l }
Treatment $A$ & 189 & 168 & 176 & 186 & 183 & 187 & 188 & \\
Treatment $B$ & 177 & 179 & 173 & 180 & 178 & 170 & 175 & 174 \\
\end{tabular}
\end{center}
Use a Wilcoxon rank sum test, at the $5 \%$ level of significance, to test whether the LDL levels of patients given treatment $B$ are lower than the LDL levels of patients given treatment $A$.
\hfill \mbox{\textit{OCR S4 2016 Q2 [8]}}