June 2024 Paper 2 Q9
9 A teacher is investigating how pupils travel to and from school each day. Pupils can either travel by bus, train, car, bicycle or walk.
The teacher decides to collect a sample of size 60 for the investigation.
Explain how collecting a sample which just consists of pupils who live in the same village as the teacher might introduce bias. [1]
The table below shows how many students there are in each year.
| Year 7 | Year 8 | Year 9 | Year 10 | Year 11 |
|---|---|---|---|---|
| 86 | 105 | 107 | 101 | 101 |
Calculate the number of pupils in the sample who are in Year 9. [2]
The teacher generates a sample of 10 pupils from the 86 in Year 7 by listing them in alphabetical order and selecting the first name on the list and every ninth name thereafter.
| Scheme | Marks | AO |
|---|---|---|
| (probably) wouldn’t include any pupils who eg cycle or eg walk to school (and hence biased towards certain methods of transport) oe | B1 | 2.2b |
| [1] |
Notes
B1: must refer to at least one of the given modes of transport
| Scheme | Marks | AO |
|---|---|---|
| \(\frac{107}{500} \times 60\) | M1 | 1.1 |
| 13 | A1 | 1.1 |
| [2] |
Notes
M1: allow slip in calculation of 500 if clearly their sum of all pupils; may be implied by 12.84 or 12.8
A1: B2 for 13 unsupported
| Scheme | Marks | AO |
|---|---|---|
| not simple random sampling because every possible sample does not have an equal probability of being selected oe | B1 | 2.4 |
| [1] |
Notes
B1: allow
eg no because not possible to select every possible sample
eg not simple random sampling because every pupil not equally likely to be selected
do not allow
eg not simple random sampling because it’s systematic sampling