| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2024 |
| Session | January |
| Marks | 8 |
| 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 clear structure: a 2×3 contingency table with given data, requiring calculation of expected frequencies, test statistic, and comparison to critical value. All steps are routine and follow a well-practiced algorithm with no conceptual challenges beyond applying the standard formula. Slightly easier than average due to straightforward setup and small table size. |
| Spec | 5.06a Chi-squared: contingency tables |
| \multirow{2}{*}{} | Type of treatment | ||
| None | Sulphur | Copper sulphate | |
| No fungus present | 20 | 55 | 48 |
| Fungus present | 10 | 8 | 9 |
\begin{enumerate}
\item Chen is treating vines to prevent fungus appearing. One month after the treatment, Chen monitors the vines to see if fungus is present.
\end{enumerate}
The contingency table shows information about the type of treatment for a sample of 150 vines and whether or not fungus is present.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
\multirow{2}{*}{} & \multicolumn{3}{|c|}{Type of treatment} \\
\hline
& None & Sulphur & Copper sulphate \\
\hline
No fungus present & 20 & 55 & 48 \\
\hline
Fungus present & 10 & 8 & 9 \\
\hline
\end{tabular}
\end{center}
Test, at the $5 \%$ level of significance, whether or not there is any association between the type of treatment and the presence of fungus.\\
Show your working clearly, stating your hypotheses, expected frequencies, test statistic and critical value.
\hfill \mbox{\textit{Edexcel S3 2024 Q1 [8]}}