| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | Confidence interval supports assertion |
| Difficulty | Standard +0.3 This is a straightforward application of the chi-squared confidence interval formula for variance with clearly stated values (n=16, s²=0.003). Part (a) requires direct substitution into a standard formula, and part (b) is a simple comparison requiring minimal interpretation. While chi-squared intervals are S4 content, the execution is mechanical with no problem-solving or conceptual challenges beyond recalling the procedure. |
| Spec | 5.05d Confidence intervals: using normal distribution |
5. 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.
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.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 2008 Q5 [8]}}