| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Paired t-test |
| Difficulty | Standard +0.3 This is a straightforward paired t-test application with clearly paired data, normal distribution stated, and standard hypothesis testing procedure at S4 level. The question requires calculating differences, performing a one-tailed paired t-test, and interpreting results—all routine techniques for this module with no conceptual challenges or novel insights needed. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Mouse | A | B | C | D | \(E\) | \(F\) | G | \(H\) | I | \(J\) |
| Weight before diet | 50.0 | 48.3 | 47.5 | 54.0 | 38.9 | 42.7 | 50.1 | 46.8 | 40.3 | 41.2 |
| Weight after diet | 52.1 | 47.6 | 50.1 | 52.3 | 42.2 | 44.3 | 51.8 | 48.0 | 41.9 | 43.6 |
\begin{enumerate}
\item The weights, in grams, of mice are normally distributed. A biologist takes a random sample of 10 mice. She weighs each mouse and records its weight.
\end{enumerate}
The ten mice are then fed on a special diet. They are weighed again after two weeks.\\
Their weights in grams are as follows:
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline
Mouse & A & B & C & D & $E$ & $F$ & G & $H$ & I & $J$ \\
\hline
Weight before diet & 50.0 & 48.3 & 47.5 & 54.0 & 38.9 & 42.7 & 50.1 & 46.8 & 40.3 & 41.2 \\
\hline
Weight after diet & 52.1 & 47.6 & 50.1 & 52.3 & 42.2 & 44.3 & 51.8 & 48.0 & 41.9 & 43.6 \\
\hline
\end{tabular}
\end{center}
Stating your hypotheses clearly, and using a $1 \%$ level of significance, test whether or not the diet causes an increase in the mean weight of the mice.\\
\hfill \mbox{\textit{Edexcel S4 2008 Q3 [8]}}