| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Standard +0.8 This S4 question requires knowledge of chi-squared distribution for variance confidence intervals, a topic less commonly practiced than mean-based inference. Students must correctly apply the formula with n-1 degrees of freedom, handle the inverted inequality when converting from variance to limits, and interpret results in context. While procedurally straightforward for well-prepared students, the chi-squared approach is more specialized than standard normal/t-distribution work, placing it moderately above average difficulty. |
| Spec | 5.05d Confidence intervals: using normal distribution |
A machine is filling bottles of milk. A random sample of 16 bottles was taken and the volume of milk in each bottle was measured and recorded. The volume of milk in a bottle is normally distributed and the unbiased estimate of the variance, $s^2$, of the volume of milk in a bottle is 0.003
\begin{enumerate}[label=(\alph*)]
\item Find a 95\% confidence interval for the variance of the population of volumes of milk from which the sample was taken.
[5]
The machine should fill bottles so that the standard deviation of the volumes is equal to 0.07
\item Comment on this with reference to your 95\% confidence interval.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q5 [8]}}