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Date May 2013 Marks available 2 Reference code 13M.1.sl.TZ2.6
Level SL only Paper 1 Time zone TZ2
Command term State 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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