| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2016 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Standard 3×3 contingency table |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with clearly presented data in a 3×3 contingency table. Students need to calculate expected frequencies, compute the test statistic using the formula, find degrees of freedom (4), and compare to critical value at 1% significance. While it requires multiple computational steps, it follows a routine procedure taught explicitly in S3 with no conceptual surprises or novel problem-solving required—making it slightly easier than the average A-level question. |
| Spec | 5.06a Chi-squared: contingency tables |
| \cline { 2 - 5 } | In favour | Neutral | Against | |
| \cline { 2 - 5 } | Democrat | 58 | 16 | 16 |
| \cline { 2 - 5 } Party | Independent | 25 | 4 | 11 |
| \cline { 2 - 5 } | Republican | 17 | 20 | 33 |
| \cline { 2 - 5 } | ||||
| \cline { 2 - 5 } |
2 A random sample of 200 American voters were asked about which political party they supported and their attitude to a proposed new form of taxation. The voters' responses are summarised in the table.
Attitude
\begin{center}
\begin{tabular}{ | l | l | c | c | c | }
\cline { 2 - 5 }
& & In favour & Neutral & Against \\
\cline { 2 - 5 }
& Democrat & 58 & 16 & 16 \\
\cline { 2 - 5 }
Party & Independent & 25 & 4 & 11 \\
\cline { 2 - 5 }
& Republican & 17 & 20 & 33 \\
\cline { 2 - 5 }
& & & & \\
\cline { 2 - 5 }
\end{tabular}
\end{center}
Carry out a $\chi ^ { 2 }$ test, at the $1 \%$ level of significance, to investigate whether there is an association between party supported and attitude to the proposed form of taxation.
\hfill \mbox{\textit{OCR S3 2016 Q2 [7]}}