S4 January 2006 Q1
1. A diabetic patient records her blood glucose readings in mmol/l at random times of day over several days. Her readings are given below.
5.3 5.7 8.4 8.7 6.3 8.0 7.2
Assuming that the blood glucose readings are normally distributed calculate
(a) an unbiased estimate for the variance \(\sigma^2\) of the blood glucose readings, (2)
(b) a 90% confidence interval for the variance \(\sigma^2\) of blood glucose readings. (5)
(c) State whether or not the confidence interval supports the assertion that \(\sigma = 0.9\).
Give a reason for your answer. (1)
Give a reason for your answer. (1)
| Scheme | Marks |
|---|---|
| \(\sum x = 49.6\,;\quad \sum x^2 = 362.36\) \(s^2 = \dfrac{1}{6}\left(362.36 - \dfrac{49.6^2}{7}\right) = 1.8180952\ldots\) awrt 1.82 | M1 A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(\text{CI} = \left(\dfrac{6 \times 1.818\ldots}{12.592},\ \dfrac{6 \times 1.818\ldots}{1.635}\right)\) | M1 |
| 12.592, 1.635 | B1 B1 |
| \(= (0.866\ldots,\ 6.67\ldots)\) awrt (0.866, 6.67) | A1 A1 |
| (5) |
| Scheme | Marks |
|---|---|
| \(0.9^2 \lt 0.866\), interval does not support \(\sigma = 0.9\) as out of range. | B1 |
| (1) | |
| (8 marks) |