| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Standard +0.8 This S4 question requires constructing a confidence interval for variance using the chi-squared distribution, which is a less commonly practiced technique than mean-based inference. Students must correctly apply the formula with (n-1)s²/σ² ~ χ²(n-1), use the appropriate chi-squared critical values, and interpret the interval. While methodical, it's more conceptually demanding than routine hypothesis tests and involves careful manipulation of inequalities. |
| Spec | 5.05d Confidence intervals: using normal distribution |
A random sample of 15 tomatoes is taken and the weight $x$ grams of each tomato is found. The results are summarised by $\sum x = 208$ and $\sum x^2 = 2962$.
\begin{enumerate}[label=(\alph*)]
\item Assuming that the weights of the tomatoes are normally distributed, calculate the 90\% confidence interval for the variance $\sigma^2$ of the weights of the tomatoes. [7]
\item State with a reason whether or not the confidence interval supports the assertion $\sigma^2 = 3$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q4 [9]}}