S2 January 2007 Q1
1.
(a) Define a statistic. (2)
A random sample \(X_1, X_2, \ldots, X_n\) is taken from a population with unknown mean \(\mu\).
(b) For each of the following state whether or not it is a statistic.
(i) \(\dfrac{X_1 + X_4}{2}\), (1)
(ii) \(\dfrac{\sum X^2}{n} - \mu^2\). (1)
| Scheme | Marks |
|---|---|
| A random variable; function of known observations (from a population). data OK | B1 B1 |
| (2) |
| Scheme | Marks |
|---|---|
| (i) Yes | B1 |
| (1) | |
| (ii) No | B1 |
| (1) | |
| (4 marks) |