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Date	May Specimen	Marks available	2	Reference code	SPM.1.sl.TZ0.8
Level	SL only	Paper	1	Time zone	TZ0
Command term	Find	Question number	8	Adapted from	N/A

Question

Members of a certain club are required to register for one of three sports, badminton, volleyball or table tennis. The number of club members of each gender choosing each sport in a particular year is shown in the table below.

A ${\chi ^2}$ (Chi-squared) test at the $5\%$ significance level is used to determine whether the choice of sport is independent of gender.

Find the expected number of female volleyball players under this hypothesis.

[2]

Write down the $p$ -value for the test.

[2]

State, with a reason, the conclusion of the test.

[2]

Markscheme

$\frac{{50}}{{120}} \times \frac{{35}}{{120}} \times 120$ OR $\left( {\frac{{50 \times 35}}{{120}}} \right)$ (M1)

$= 14.6$ ( $14.5833 \ldots$ ) (A1) (C2)

$0.0746$ (A2) (C2)

Since $p{\text{-value}} > 5\%$ , the choice of the sport is independent of gender. (R1)(A1)(ft) (C2)

Note: The (R1) is awarded for the explicit comparison, the (A1)(ft) is awarded for a consistent conclusion with their answer in part (c).
It is therefore possible that (R1)(A0) may be awarded, but (R0)(A1) can never be awarded.

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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