| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2010 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Standard 2×2 contingency table |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with a 2×2 contingency table requiring calculation of expected frequencies, test statistic, and comparison with critical values at two significance levels. While it involves multiple steps, the procedure is routine and well-practiced in S3, with no conceptual challenges beyond applying the standard formula and interpreting results. |
| Spec | 5.06a Chi-squared: contingency tables |
| City dweller | Country dweller | |
| Saturday shopper | 23 | 19 |
| Sunday shopper | 42 | 16 |
3 The developers of a shopping mall sponsored a study of the shopping habits of its users. Each of a random sample of 100 users was asked whether their weekend shopping was mainly on Saturday or mainly on Sunday. The results, classified according to whether the user lived in the city or the country, are shown in the table.
\begin{center}
\begin{tabular}{ | l | c | c | }
\hline
& City dweller & Country dweller \\
\hline
Saturday shopper & 23 & 19 \\
\hline
Sunday shopper & 42 & 16 \\
\hline
\end{tabular}
\end{center}
(i) Test, at the $10 \%$ significance level, whether there is an association between the area in which shoppers live and the day on which they shop at the weekend.\\
(ii) State, with a reason, whether the conclusion of the test would be different at the $3 \%$ significance level.
\hfill \mbox{\textit{OCR S3 2010 Q3 [9]}}