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

Find the number of degrees of freedom for this test.

[2]

Write down the critical value for this test.

[1]

State the conclusion of this test. Give a reason for your decision.

[2]

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”.

$(2 - 1)(5-1)$ (M1)

Note: Award (M1) for correct substitution in the correct formula.

$= 4$ (A1) (C2)

9.488 (A1)(ft) (C1)

Notes: Follow through from their answer to part (b). Accept 9.49.

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).

Examiners report

[N/A]

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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