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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 Write down 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]
a.

Write down the \(p\)-value for the test.

[2]
b.

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

[2]
c.

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)

a.

\(0.0746\)     (A2)     (C2)

b.

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.

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

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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