| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | June |
| Marks | 8 |
| 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. Students need to state hypotheses, calculate expected frequencies, compute the chi-squared statistic, compare with critical value, and conclude. While it requires multiple steps, it's a routine application of a core S2 technique with no conceptual surprises, making it slightly easier than average. |
| Spec | 5.06a Chi-squared: contingency tables |
| Sickness | No sickness | Total | |
| Drug taken | 24 | 56 | 80 |
| No drug taken | 11 | 9 | 20 |
| Total | 35 | 65 | 100 |
It is claimed that a new drug is effective in the prevention of sickness in holiday-makers. A sample of $100$ holiday-makers was surveyed, with the following results.
\begin{center}
\begin{tabular}{|l|c|c|c|}
\hline
& Sickness & No sickness & Total \\
\hline
Drug taken & 24 & 56 & 80 \\
\hline
No drug taken & 11 & 9 & 20 \\
\hline
Total & 35 & 65 & 100 \\
\hline
\end{tabular}
\end{center}
Assuming that the $100$ holiday-makers are a random sample, use a $\chi^2$ test, at the $5\%$ level of significance, to investigate the claim. [8 marks]
\hfill \mbox{\textit{AQA S2 2010 Q2 [8]}}