| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2014 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Interpret association after test |
| Difficulty | Moderate -0.3 This is a standard chi-squared test of independence with straightforward calculations. Part (a) requires simple percentage-to-frequency conversion, part (b) is a routine application of the chi-squared test procedure (calculate expected values, compute test statistic, compare to critical value), and part (c) asks for basic interpretation. The question is slightly easier than average because it's highly structured with clear steps and uses a common significance level, though it does require careful arithmetic with the 250 sample size. |
| Spec | 5.06a Chi-squared: contingency tables |
| \cline { 2 - 5 } \multicolumn{1}{c|}{} | England | Scotland | Wales |
| ||
| Male | 22.8 | 17.6 | 10.8 | 6.8 | ||
| Female | 15.6 | 17.2 | 7.6 | 1.6 |
| England | Scotland | Wales | Northern Ireland | Total | |
| Male | 145 | ||||
| Female | 105 | ||||
| Total | 250 |
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Please provide the full mark scheme content that needs to be cleaned up, and I'll convert the unicode symbols to LaTeX notation and format it clearly with marking annotations preserved.2 A large multinational company recruits employees from all four countries in the UK. For a sample of 250 recruits, the percentages of males and females from each of the countries are shown in Table 1.
\begin{table}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Table 1}
\begin{tabular}{ | l | c | c | c | c | }
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & England & Scotland & Wales & \begin{tabular}{ c }
Northern \\
Ireland \\
\end{tabular} \\
\hline
Male & 22.8 & 17.6 & 10.8 & 6.8 \\
\hline
Female & 15.6 & 17.2 & 7.6 & 1.6 \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Add the frequencies to the contingency table, Table 2, below.
\item Carry out a $\chi ^ { 2 }$-test at the $10 \%$ significance level to investigate whether there is an association between country and gender of recruits.
\item By comparing observed and expected values, make one comment about the distribution of female recruits.\\[0pt]
[1 mark]
\begin{table}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Table 2}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
& England & Scotland & Wales & Northern Ireland & Total \\
\hline
Male & & & & & 145 \\
\hline
Female & & & & & 105 \\
\hline
Total & & & & & 250 \\
\hline
\end{tabular}
\end{center}
\end{table}
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2014 Q2 [11]}}