| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2016 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Standard 2×3 contingency table |
| Difficulty | Moderate -0.3 This is a standard chi-squared test of independence with a 2×3 contingency table requiring routine calculation of expected frequencies, test statistic, and comparison with critical value. Part (b) requires identifying the largest contribution to chi-squared. While it involves multiple steps, it follows a completely standard template taught in S3 with no novel problem-solving or conceptual challenges beyond applying the learned procedure. |
| Spec | 5.06a Chi-squared: contingency tables |
| \multirow{2}{*}{} | Driving test centre | \multirow{2}{*}{Total} | |||
| \(\boldsymbol { A }\) | B | C | |||
| \multirow{2}{*}{Result} | Pass | 99 | 110 | 68 | 277 |
| Fail | 108 | 116 | 119 | 343 | |
| Total | 207 | 226 | 187 | 620 | |
2. A researcher investigates the results of candidates who took their driving test at one of three driving test centres.
A random sample of 620 candidates gave the following results.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{\multirow{2}{*}{}} & \multicolumn{3}{|c|}{Driving test centre} & \multirow{2}{*}{Total} \\
\hline
& & $\boldsymbol { A }$ & B & C & \\
\hline
\multirow{2}{*}{Result} & Pass & 99 & 110 & 68 & 277 \\
\hline
& Fail & 108 & 116 & 119 & 343 \\
\hline
\multicolumn{2}{|c|}{Total} & 207 & 226 & 187 & 620 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Test, at the $5 \%$ level of significance, whether there is an association between the results of candidates' driving tests and the driving test centre. State your hypotheses and show your working clearly. You should state your expected frequencies correct to 2 decimal places.
The researcher decides to conduct a further investigation into the results of candidates' driving tests.
\item State which driving test centre you would recommend for further investigation. Give a reason for your answer.
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2016 Q2 [12]}}