| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Type I / Type II error interpretation |
| Difficulty | Moderate -0.3 This is a standard chi-squared test of independence with a 2×2 contingency table, requiring routine calculation of expected frequencies, test statistic, and comparison with critical value. Part (b) asks for basic interpretation of Type I error. While it requires multiple steps, all procedures are textbook-standard with no novel insight needed, making it slightly easier than average. |
| Spec | 5.06a Chi-squared: contingency tables |
| Salary < £30000 | Salary \(\boldsymbol { \geq }\) £30000 | Total | |
| University education | 52 | 78 | 130 |
| No university education | 63 | 57 | 120 |
| Total | 115 | 135 | 250 |
6 A survey is carried out in an attempt to determine whether the salary achieved by the age of 30 is associated with having had a university education.
The results of this survey are given in the table.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
& Salary < £30000 & Salary $\boldsymbol { \geq }$ £30000 & Total \\
\hline
University education & 52 & 78 & 130 \\
\hline
No university education & 63 & 57 & 120 \\
\hline
Total & 115 & 135 & 250 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Use a $\chi ^ { 2 }$ test, at the $10 \%$ level of significance, to determine whether the salary achieved by the age of 30 is associated with having had a university education.
\item What do you understand by a Type I error in this context?
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2008 Q6 [11]}}