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Date	November 2013	Marks available	2	Reference code	13N.1.sl.TZ0.8
Level	SL only	Paper	1	Time zone	TZ0
Command term	State	Question number	8	Adapted from	N/A

Question

$180$ spectators at a swimming championship were asked which, of four swimming styles, was the one they preferred to watch.

The results of their responses are shown in the table.

A ${\chi ^2}$ test was conducted at the $5\%$ significance level.

Write down the null hypothesis for this test.

[1]

Write down the number of degrees of freedom.

[1]

Write down the value of $\chi _{calc}^2$ .

[2]

The critical value, at the $5\%$ significance level, is $7.815$ .

State, giving a reason, the conclusion to the test.

[2]

Markscheme

The (preferred) swimming style is independent of gender (A1) (C1)

Notes: Accept “not associated”. Do not accept “not related”, “not correlated” or “not influenced”.

[1 mark]

$3$ (A1) (C1)

[1 mark]

$\chi _{calc}^2 = 16.4{\text{ (16.4285}} \ldots {\text{)}}$ (A2) (C2)

[2 marks]

Do not accept the Null Hypothesis (Reject the Null Hypothesis).

$\chi _{calc}^2 > \chi _{crit}^2$ OR $16.4 > 7.815$ (R1)(A1)(ft)

Do not accept the Null Hypothesis (Reject the Null Hypothesis).

$p$ -value of ${\text{9.26148}} \ldots \times {10^{ - 4}} < 0.05$ (R1)(A1)(ft) (C2)

Notes: Follow through from their answer to part (c).

Accept “(preferred) swimming style is not independent (dependent) of gender” as the conclusion.

Do not award (R0)(A1).

If using the $p$ -value the value must be seen.

[2 marks]

Examiners report

This question was well answered by the majority of the candidates, many scoring the mark.

This question was well answered by the majority of the candidates, many scoring both marks.

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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