| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2011 |
| 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 clearly labeled hypotheses, straightforward calculation of expected frequencies (2×3 table), and comparison with critical value. While it requires multiple computational steps and proper statistical conclusion, it follows a routine procedure taught directly in S3 with no conceptual surprises or novel problem-solving required. |
| Spec | 5.06a Chi-squared: contingency tables |
| \(D_1\) | \(D_2\) | |
| First shift | 45 | 18 |
| Second shift | 55 | 20 |
| Third shift | 50 | 12 |
A factory manufactures batches of an electronic component. Each component is manufactured in one of three shifts. A component may have one of two types of defect, $D_1$ or $D_2$, at the end of the manufacturing process. A production manager believes that the type of defect is dependent upon the shift that manufactured the component. He examines 200 randomly selected defective components and classifies them by defect type and shift. The results are shown in the table below.
\begin{tabular}{|c|c|c|}
\hline
& $D_1$ & $D_2$ \\
\hline
First shift & 45 & 18 \\
\hline
Second shift & 55 & 20 \\
\hline
Third shift & 50 & 12 \\
\hline
\end{tabular}
Stating your hypotheses, test, at the 10\% level of significance, whether or not there is evidence to support the manager's belief. Show your working clearly.
[10]
\hfill \mbox{\textit{Edexcel S3 2011 Q3 [10]}}