Chi-squared confidence interval for variance

A question is this type if and only if it asks to construct a confidence interval for a single population variance using the chi-squared distribution, given either raw data or summary statistics from one sample.

1 questions · Standard +0.3

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Edexcel S4 2006 January Q1
8 marks Standard +0.3
  1. 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
  1. an unbiased estimate for the variance \(\sigma ^ { 2 }\) of the blood glucose readings,
  2. a \(90 \%\) confidence interval for the variance \(\sigma ^ { 2 }\) of blood glucose readings.
  3. State whether or not the confidence interval supports the assertion that \(\sigma = 0.9\). Give a reason for your answer.