| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2006 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Interpret association after test |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with clearly presented data in a 2×4 contingency table. Students must calculate expected frequencies, compute the test statistic using the standard formula, compare to critical values, and interpret the result. While it requires multiple steps and careful calculation, it follows a completely routine procedure taught in S2 with no novel problem-solving or conceptual challenges beyond applying the standard algorithm. |
| Spec | 5.06a Chi-squared: contingency tables |
| Squash | Badminton | Archery | Hockey | Total | |
| Male | 5 | 16 | 30 | 19 | 70 |
| Female | 4 | 20 | 33 | 53 | 110 |
| Total | 9 | 36 | 63 | 72 | 180 |
| Answer | Marks | Guidance |
|---|---|---|
| \(H_0\): Choice independent of gender | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| S & B | Archery | Hockey |
| Male | 21/17.5 | 30/24.5 |
| Female | 24/27.5 | 33/38.5 |
| M1, M1 | \(E_i < 5\) (Similar categories) |
| Answer | Marks | Guidance |
|---|---|---|
| S & B | Archery | Hockey |
| Male | 0.7000 | 1.2347 |
| Female | 0.4455 | 0.7857 |
| M1 | ||
| \(\chi^2_{\text{calc}} = 7.90\) | A1 | |
| \(\nu = 2\) | B1 | |
| \(\chi^2_{\text{5%}}(2) = 5.991\) | B1ft | |
| Reject \(H_0\) | A1ft |
| Answer | Marks | Guidance |
|---|---|---|
| More females and fewer males chose to participate in hockey than expected | B1, B1 | 2 marks |
**2(a)**
$H_0$: Choice independent of gender | B1 | | gender not associated with choice
Contingency table with combined categories:
| | S & B | Archery | Hockey |
|---|---|---|---|
| Male | 21/17.5 | 30/24.5 | 19/28 |
| Female | 24/27.5 | 33/38.5 | 53/44 |
| M1, M1 | | $E_i < 5$ (Similar categories)
$\chi^2$ values:
| | S & B | Archery | Hockey |
|---|---|---|---|
| Male | 0.7000 | 1.2347 | 2.8928 |
| Female | 0.4455 | 0.7857 | 1.8409 |
| M1 | |
$\chi^2_{\text{calc}} = 7.90$ | A1 | | (7.8 to 7.9)
$\nu = 2$ | B1 | |
$\chi^2_{\text{5%}}(2) = 5.991$ | B1ft | | (on their ν)
Reject $H_0$ | A1ft | | reject $H_0$ and $H_1$ stated or statement in context | 10 marks
**2(b)**
More females and fewer males chose to participate in hockey than expected | B1, B1 | 2 marks
**Question 2 Total: 12 marks**
---2 Year 12 students at Newstatus School choose to participate in one of four sports during the Spring term.
The students' choices are summarised in the table.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
& Squash & Badminton & Archery & Hockey & Total \\
\hline
Male & 5 & 16 & 30 & 19 & 70 \\
\hline
Female & 4 & 20 & 33 & 53 & 110 \\
\hline
Total & 9 & 36 & 63 & 72 & 180 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Use a $\chi ^ { 2 }$ test, at the $5 \%$ level of significance, to determine whether the choice of sport is independent of gender.
\item Interpret your result in part (a) as it relates to students choosing hockey.
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2006 Q2 [12]}}