| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2013 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Type I / Type II error interpretation |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with a 2×2 contingency table, requiring calculation of expected frequencies, test statistic, and comparison to critical value. Part (b) tests understanding of Type I/II errors in a straightforward context. Slightly easier than average due to small table size and routine application of the test procedure. |
| Spec | 5.06a Chi-squared: contingency tables |
| Applied for grant | Did not apply for grant | Total | |
| Letter | 30 | 130 | 160 |
| Phone call | 14 | 26 | 40 |
| Total | 44 | 156 | 200 |
2 A town council wanted residents to apply for grants that were available for home insulation. In a trial, a random sample of 200 residents was encouraged, either in a letter or by a phone call, to apply for the grants. The outcomes are shown in the table.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
& Applied for grant & Did not apply for grant & Total \\
\hline
Letter & 30 & 130 & 160 \\
\hline
Phone call & 14 & 26 & 40 \\
\hline
Total & 44 & 156 & 200 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item The council believed that a phone call was more effective than a letter in encouraging people to apply for a grant. Use a $\chi ^ { 2 }$-test to investigate this belief at the $5 \%$ significance level.
\item After the trial, all the residents in the town were encouraged, either in a letter or by a phone call, to apply for the grants. It was found that there was no association between the method of encouragement and the outcome. State, with a reason, whether a Type I error, a Type II error or neither occurred in carrying out the test in part (a).\\
(2 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2013 Q2 [10]}}