| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2013 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Cell combining required |
| Difficulty | Moderate -0.3 This is a standard chi-squared test of independence with straightforward application of the test procedure. The main challenge is recognizing that expected frequencies are too small (requiring column combination), but this is a routine check in S2. The interpretation in part (b) requires only basic observation of the data rather than complex statistical reasoning. |
| Spec | 5.06a Chi-squared: contingency tables |
| \multirow{2}{*}{} | Type of property | ||||
| Flat | Terraced | Semidetached | Detached | Total | |
| Sold within three months | 4 | 34 | 28 | 18 | 84 |
| Sold in more than three months | 9 | 18 | 8 | 6 | 41 |
| Total | 13 | 52 | 36 | 24 | 125 |
2 A large estate agency would like all the properties that it handles to be sold within three months. A manager wants to know whether the type of property affects the time taken to sell it. The data for a random sample of properties sold are tabulated below.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\multirow{2}{*}{} & \multicolumn{4}{|c|}{Type of property} & \\
\hline
& Flat & Terraced & Semidetached & Detached & Total \\
\hline
Sold within three months & 4 & 34 & 28 & 18 & 84 \\
\hline
Sold in more than three months & 9 & 18 & 8 & 6 & 41 \\
\hline
Total & 13 & 52 & 36 & 24 & 125 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Conduct a $\chi ^ { 2 }$-test, at the $10 \%$ level of significance, to determine whether there is an association between the type of property and the time taken to sell it. Explain why it is necessary to combine two columns before carrying out this test.
\item The manager plans to spend extra money on advertising for one type of property in an attempt to increase the number sold within three months. Explain why the manager might choose:
\begin{enumerate}[label=(\roman*)]
\item terraced properties;
\item flats.\\
(2 marks)
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA S2 2013 Q2 [12]}}