| Date | May 2012 | Marks available | 2 | Reference code | 12M.1.sl.TZ2.8 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 8 | Adapted from | N/A |
Question
A researcher consulted 500 men and women to see if the colour of the car they drove was independent of gender. A \(\chi^2\) test for independence was carried out.
Write down the null hypothesis.
[1]
a.
The colours of the cars were red, green, blue, black and silver.
Find the number of degrees of freedom for this test.
[2]
b.
At the 5 % significance level the \(\chi_{calc}^2\) was found to be 8.73.
Write down the critical value, \(\chi_{crit}^2\), for this test.
[1]
c.
Markscheme
Colour of car is independent of gender. (Colour of car and gender are independent) (A1) (C1)
Note: Accept “not associated”. Do not accept “not related”, “not correlated” or “not linked”.
[1 mark]
a.
(2 − 1)(5 − 1) = 4 (M1)(A1) (C2)
[2 marks]
b.
\(\chi_{crit}^2 = 9.488\) (A1)(ft) (C1)
Notes: Accept 9.49. Follow through from part (b).
[1 mark]
c.
Examiners report
This question was well answered by the majority of the candidates, many scoring the maximum number of marks. It was disappointing to see the number of candidates who left this question blank.
a.
This question was well answered by the majority of the candidates, many scoring the maximum number of marks. It was disappointing to see the number of candidates who left this question blank.
b.
This question was well answered by the majority of the candidates, many scoring the maximum number of marks. It was disappointing to see the number of candidates who left this question blank.
c.
Syllabus sections
Topic 4 - Statistical applications » 4.4 » The \({\chi ^2}\) test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; degrees of freedom; \(p\)-values.
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