| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Paired sample t-test |
| Difficulty | Standard +0.3 This is a standard paired t-test question with clearly structured data. Students must calculate differences, find mean and standard deviation of differences, then perform a one-tailed hypothesis test. While it requires multiple computational steps and proper hypothesis formulation, it follows a routine S4 procedure with no conceptual surprises or novel problem-solving required. Slightly easier than average due to its straightforward setup and clear signposting. |
| 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 |
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.
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{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\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}
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.
[8]
\hfill \mbox{\textit{Edexcel S4 Q3 [8]}}