S4 June 2008 Q4
4. A town council is concerned that the mean price of renting two bedroom flats in the town has exceeded £650 per month. A random sample of eight two bedroom flats gave the following results, £\(x\), per month.
705, 640, 560, 680, 800, 620, 580, 760
[You may assume \(\sum x = 5345 \qquad \sum x^2 = 3621025\)]
(a) Find a 90% confidence interval for the mean price of renting a two bedroom flat. (6)
(b) State an assumption that is required for the validity of your interval in part (a). (1)
(c) Comment on whether or not the town council is justified in being concerned. Give a reason for your answer. (2)
| Scheme | Marks |
|---|---|
| \(\bar{x} = 668.125 \quad s = 84.428\) | M1 M1 |
| \(T_7(5\%) = 1.895\) | B1 |
| Confidence limits \(= 668.125 \pm \dfrac{1.895 \times 84.428}{\sqrt{8}}\) | M1 |
| \(= 611.6\) and \(724.7\) Confidence interval \(= (612,\ 725)\) | A1 A1 |
| (6) |
| Scheme | Marks |
|---|---|
| Normal distribution | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| £650 is within the confidence interval. No need to worry. | B1ft B1ft |
| (2) |