| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2010 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Standard 2×3 contingency table |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with a 2×3 contingency table. Students must calculate expected frequencies, compute the test statistic, and compare to critical values—all routine S3 procedures. The calculation is straightforward with no conceptual surprises, making it slightly easier than average. |
| Spec | 5.06a Chi-squared: contingency tables |
| Annual income Finances | Worse | Same | Better |
| Under \(\pounds 15000\) | 14 | 11 | 9 |
| \(\pounds 15000\) and above | 17 | 20 | 29 |
\begin{enumerate}
\item A random sample of 100 people were asked if their finances were worse, the same or better than this time last year. The sample was split according to their annual income and the results are shown in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | l | c | c | c | }
\hline
Annual income Finances & Worse & Same & Better \\
\hline
Under $\pounds 15000$ & 14 & 11 & 9 \\
\hline
$\pounds 15000$ and above & 17 & 20 & 29 \\
\hline
\end{tabular}
\end{center}
Test, at the $5 \%$ level of significance, whether or not the relative state of their finances is independent of their income range. State your hypotheses and show your working clearly.
\hfill \mbox{\textit{Edexcel S3 2010 Q5 [10]}}