- 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.
$$\begin{array} { l l l l l l l }
5.3 & 5.7 & 8.4 & 8.7 & 6.3 & 8.0 & 7.2
\end{array}$$
Assuming that the blood glucose readings are normally distributed calculate
- an unbiased estimate for the variance \(\sigma ^ { 2 }\) of the blood glucose readings,
- a \(90 \%\) confidence interval for the variance \(\sigma ^ { 2 }\) of blood glucose readings.
- State whether or not the confidence interval supports the assertion that \(\sigma = 0.9\).
Give a reason for your answer.