| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2011 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Percentages given, table construction required |
| Difficulty | Standard +0.3 This is a straightforward chi-squared test of independence with clearly structured data. Part (a) requires simple percentage calculations to convert to frequencies, and part (b) is a standard application of the chi-squared test procedure with expected frequencies, test statistic calculation, and comparison to critical values. The question is slightly easier than average because the data is well-organized and the method is routine, though it does require careful arithmetic across multiple steps. |
| Spec | 5.06a Chi-squared: contingency tables |
| Conservative | Labour | Liberal Democrat | Other parties | |
| Male | 32.5 | 30 | 25 | 12.5 |
| Female | 40 | 25 | 20 | 15 |
| Conservative | Labour | Liberal Democrat | Other parties | Total | |
| Male | 480 | ||||
| Female | 540 | ||||
| Total | 1020 |
2 It is claimed that the way in which students voted at a particular general election was independent of their gender.
In order to investigate this claim, 480 male and 540 female students who voted at this general election were surveyed. These students may be regarded as a random sample.
The percentages of males and females who voted for the different parties are recorded in the table.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
& Conservative & Labour & Liberal Democrat & Other parties \\
\hline
Male & 32.5 & 30 & 25 & 12.5 \\
\hline
Female & 40 & 25 & 20 & 15 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Complete the contingency table below.
\item Hence determine, at the $1 \%$ level of significance, whether the way in which students voted at this general election was independent of their gender.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
& Conservative & Labour & Liberal Democrat & Other parties & Total \\
\hline
Male & & & & & 480 \\
\hline
Female & & & & & 540 \\
\hline
Total & & & & & 1020 \\
\hline
\end{tabular}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2011 Q2 [11]}}