| 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]
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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