| Exam Board | WJEC |
|---|---|
| Module | Further Unit 5 (Further Unit 5) |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Wilcoxon matched-pairs signed-rank test |
| Difficulty | Standard +0.8 This is a Further Maths statistics question requiring execution of a Wilcoxon signed rank test with paired data. While the procedure is systematic (calculate differences, rank absolute values, sum ranks, compare to critical value), it involves multiple careful steps with potential for arithmetic errors and requires knowledge of a non-standard test. The conceptual demand is moderate but the procedural complexity and specialist nature place it above average difficulty. |
| Spec | 5.07a Non-parametric tests: when to use5.07b Sign test: and Wilcoxon signed-rank |
| Patient | A | B | C | D | E | F | G | H | I | J |
| Method A | 121 | 133 | 119 | 142 | 151 | 139 | 161 | 148 | 151 | 125 |
| Method B | 126 | 131 | 127 | 152 | 145 | 151 | 157 | 155 | 160 | 126 |
| Answer | Marks | Guidance |
|---|---|---|
| The differences are 5 −2 8 10 −6 12 −4 7 9 1 | B1 | AO3 |
| The signs may be omitted at this stage. The ranks are 4 2 7 9 5 10 3 6 8 1 | M1 | AO3 |
| A1 | AO1 | |
| \(W = \text{Sum of positive ranks} = 4 + 7 + 9 + 10 + 6 + 8 + 1 = 45\) | M1 | AO3 |
| A1 | AO1 | |
| The critical value is 44. | B1 | AO1 |
| Answer | Marks | Guidance |
|---|---|---|
| The conclusion at this significance level is that Method B gives on average a higher reading than Method A because 45 > 44 | B1 | AO3 |
| E1 | AO2 | |
| [8] |
## 6(a)
The differences are 5 −2 8 10 −6 12 −4 7 9 1 | B1 | AO3 |
The signs may be omitted at this stage. The ranks are 4 2 7 9 5 10 3 6 8 1 | M1 | AO3 | Attempting to rank absolute values; All correct
| A1 | AO1 |
$W = \text{Sum of positive ranks} = 4 + 7 + 9 + 10 + 6 + 8 + 1 = 45$ | M1 | AO3 |
| A1 | AO1 |
The critical value is 44. | B1 | AO1 |
## 6(b)
The conclusion at this significance level is that Method B gives on average a higher reading than Method A because 45 > 44 | B1 | AO3 |
| E1 | AO2 |
| [8] | |A medical student is investigating two different methods, A and B, of measuring a patient's blood pressure. He believes that Method B gives, on average, a higher reading than Method A so he defines the following hypotheses.
$H_0$: There is on average no difference in the readings obtained using Methods A and B;
$H_1$: The reading obtained using Method B is on average higher than the reading obtained using Method A.
He selects 10 patients at random and he measures their blood pressures using both methods. He obtains the following results.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Patient & A & B & C & D & E & F & G & H & I & J \\
\hline
Method A & 121 & 133 & 119 & 142 & 151 & 139 & 161 & 148 & 151 & 125 \\
\hline
Method B & 126 & 131 & 127 & 152 & 145 & 151 & 157 & 155 & 160 & 126 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Carry out an appropriate Wilcoxon signed rank test on this data set, using a 5% significance level. [6]
\item State what conclusion the medical student should reach, justifying your answer. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 5 Q6 [8]}}