| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Single sample t-test |
| Difficulty | Standard +0.3 This is a straightforward application of a one-sample t-test with clearly stated hypotheses (H₀: μ = 1012 vs H₁: μ ≠ 1012). Students must calculate sample mean and standard deviation from summary statistics, then perform a standard two-tailed test. While it requires multiple computational steps, it follows a routine procedure with no conceptual challenges or novel insights required—slightly easier than average for S4 level. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
\begin{enumerate}
\item Historical records from a large colony of squirrels show that the weight of squirrels is normally distributed with a mean of 1012 g . Following a change in the diet of squirrels, a biologist is interested in whether or not the mean weight has changed.
\end{enumerate}
A random sample of 14 squirrels is weighed and their weights $x$, in grams, recorded. The results are summarised as follows:
$$\Sigma x = 13700 , \quad \Sigma x ^ { 2 } = 13448750 .$$
Stating your hypotheses clearly test, at the $5 \%$ level of significance, whether or not there has been a change in the mean weight of the squirrels.\\
\hfill \mbox{\textit{Edexcel S4 2006 Q1 [7]}}