S3 June 2006 Q6
6. A research worker studying colour preference and the age of a random sample of 50 children obtained the results shown below.
| Age in years | Red | Blue | Totals |
|---|---|---|---|
| 4 | 12 | 6 | 18 |
| 8 | 10 | 7 | 17 |
| 12 | 6 | 9 | 15 |
| Totals | 28 | 22 | 50 |
Using a 5% significance level, carry out a test to decide whether or not there is an association between age and colour preference. State your hypotheses clearly. (11)
| Scheme | Marks | |||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\mathrm{H}_0\) : No association between age and colour (independent) | B1 | |||||||||||||||||||||
| \(\mathrm{H}_1\) : Association between age and colour (Not independent) | B1 | |||||||||||||||||||||
\(\dfrac{(O - E)^2}{E}\) 3sf or better | M1 A1 M1 A1 | |||||||||||||||||||||
| \(\displaystyle\sum \frac{(O - E)^2}{E} = 2.4446\ldots\) \(\sum\), awrt 2.44 | M1 A1 | |||||||||||||||||||||
| \(\nu = (3 - 1)(2 - 1) = 2\), \(\chi^2_2 = 5.991\) | B1 B1ft | |||||||||||||||||||||
| Insufficient evidence to reject \(\mathrm{H}_0\). No association between age and colour | A1ft | |||||||||||||||||||||
| (11) | ||||||||||||||||||||||
| (11 marks) |
Notes
(cv from correct table for ft)