| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2014 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Paired t-test |
| Difficulty | Standard +0.3 This is a straightforward application of the Wilcoxon signed-rank test with clear paired data. Students must calculate differences, rank them, and compare to critical values from tables. While it requires careful execution of the procedure, it's a standard textbook exercise with no novel insight required, making it slightly easier than average for an S4 module question. |
| Spec | 5.07b Sign test: and Wilcoxon signed-rank5.07d Paired vs two-sample: selection |
| Level of pepper extract that triggers coughing | ||||||||
| Patient | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| Standard medicine | 46 | 12 | 18 | 31 | 23 | 16 | 27 | 9 |
| New medicine | 53 | 16 | 13 | 49 | 11 | 34 | 38 | 22 |
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\item In a trial for a new cough medicine, a random sample of 8 healthy patients were given steadily increasing doses of a pepper extract until they started coughing. The level of pepper that triggered the coughing was recorded. Each patient completed the trial after taking a standard cough medicine and, at a later time, after taking the new medicine. The results are given in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | }
\hline
& \multicolumn{8}{|c|}{Level of pepper extract that triggers coughing} \\
\hline
Patient & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ \\
\hline
Standard medicine & 46 & 12 & 18 & 31 & 23 & 16 & 27 & 9 \\
\hline
New medicine & 53 & 16 & 13 & 49 & 11 & 34 & 38 & 22 \\
\hline
\end{tabular}
\end{center}
(a) Using a suitable test, at the $5 \%$ level of significance, state whether or not, on the basis of this trial, you would recommend using the new medicine. State your hypotheses clearly.\\
(b) State an assumption needed to carry out this test.\\
\hfill \mbox{\textit{Edexcel S4 2014 Q1 [9]}}