| Date | May 2013 | Marks available | 2 | Reference code | 13M.1.sl.TZ2.6 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 6 | Adapted from | N/A |
Question
A market researcher surveyed men and women about their preferred holiday destination. The holiday destinations were Antigua, Barbados, Cuba, Guadeloupe and Jamaica. A \(\chi^2\) test for independence was conducted at the 5 % significance level.
The \(\chi^2\) calculated value was found to be 8.73.
Write down the null hypothesis.
[1]
a.
Find the number of degrees of freedom for this test.
[2]
b.
Write down the critical value for this test.
[1]
c.
State the conclusion of this test. Give a reason for your decision.
[2]
d.
Markscheme
Holiday destination is independent of gender. (A1) (C1)
Note: Accept gender is independent of holiday destination, accept “not associated”, do not accept “not correlated”.
a.
\((2 - 1)(5-1)\) (M1)
Note: Award (M1) for correct substitution in the correct formula.
\(= 4\) (A1) (C2)
b.
9.488 (A1)(ft) (C1)
Notes: Follow through from their answer to part (b). Accept 9.49.
c.
Accept the null hypothesis or Accept H0. (A1)(ft)
Note: Accept gender is independent of holiday destination.
\(\chi_{({\text{calc}})}^2 < \chi_{({\text{crit}})}^2\) or 8.73 < 9.488 (R1) (C2)
Notes: Do not award (A1)(R0). Follow through from their answer in part (c).
d.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.
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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