| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2009 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Larger contingency table (4+ categories) |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with clear structure: calculate expected frequencies, compute test statistic, compare to critical value. It's slightly above average difficulty due to the 4×2 table requiring multiple calculations and careful organization, but follows a completely routine procedure with no conceptual challenges or novel elements. |
| Spec | 5.06a Chi-squared: contingency tables |
| \cline { 2 - 5 } \multicolumn{1}{c|}{} | Bulgarian |
| Finance | Polish | ||
| Male | 7 | 31 | 25 | 40 | ||
| Female | 2 | 24 | 22 | 19 |
1 Fortune High School gave its students a wider choice of subjects to study. The table shows the number of students, of each gender, who chose to study each of the additional subjects during the school year 2007/08.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & Bulgarian & \begin{tabular}{ c }
Climate \\
Change \\
\end{tabular} & Finance & Polish \\
\hline
Male & 7 & 31 & 25 & 40 \\
\hline
Female & 2 & 24 & 22 & 19 \\
\hline
\end{tabular}
\end{center}
Assuming that these data form a random sample, use a $\chi ^ { 2 }$ test, at the $10 \%$ level of significance, to test whether the choice of these subjects is independent of gender.\\
(11 marks)
\hfill \mbox{\textit{AQA S2 2009 Q1 [11]}}