| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2006 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | Chi-squared confidence interval for variance |
| Difficulty | Standard +0.3 This is a straightforward application of chi-squared confidence intervals for variance with clear steps: calculate sample variance, look up chi-squared critical values, and apply the standard formula. The interpretation in part (c) is routine. Slightly above average difficulty due to the S4 Further Maths context and chi-squared distribution being less familiar than normal/t-distributions, but the question is entirely procedural with no conceptual challenges. |
| Spec | 5.05b Unbiased estimates: of population mean and variance |
\begin{enumerate}
\item A diabetic patient records her blood glucose readings in $\mathrm { mmol } / \mathrm { l }$ at random times of day over several days. Her readings are given below.
\end{enumerate}
$$\begin{array} { l l l l l l l }
5.3 & 5.7 & 8.4 & 8.7 & 6.3 & 8.0 & 7.2
\end{array}$$
Assuming that the blood glucose readings are normally distributed calculate\\
(a) an unbiased estimate for the variance $\sigma ^ { 2 }$ of the blood glucose readings,\\
(b) a $90 \%$ confidence interval for the variance $\sigma ^ { 2 }$ of blood glucose readings.\\
(c) State whether or not the confidence interval supports the assertion that $\sigma = 0.9$.
Give a reason for your answer.\\
\hfill \mbox{\textit{Edexcel S4 2006 Q1 [8]}}