S3 January 2006 Q1
1. A school has 15 classes and a sixth form. In each class there are 30 students. In the sixth form there are 150 students. There are equal numbers of boys and girls in each class. There are equal numbers of boys and girls in the sixth form. The head teacher wishes to obtain the opinions of the students about school uniforms.
Explain how the head teacher would take a stratified sample of size 40. (7)
| Scheme | Marks |
|---|---|
| Total in School = \((15 \times 30) + 150 = 600\) | B1 |
| random sample of \(\dfrac{30}{600} \times 40\) (Use of \(\dfrac{40}{\text{their } 600}\)) \(= \underline{2}\) from each of the 15 classes | M1 A1 |
| random sample of \(\dfrac{150}{600} \times 40\) Either \(= \underline{10}\) from sixth form; | A1 |
| Label the boys in each class from 1 – 15 and the girls from 1 – 15. use random numbers to select 1 girl and 1 boy | B1 B1 |
| Label the boys in the sixth form from 1 – 75 and the girls from 1 – 75. use random numbers to select 5 different boys and 5 different girls. | B1 |
| (7) | |
| (7 marks) |