| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | Chi-squared test of independence |
| Type | Standard 2×2 contingency table |
| Difficulty | Standard +0.3 This is a standard chi-squared test for independence with a 2×2 contingency table. Students need to state hypotheses, calculate expected frequencies, compute the test statistic, compare to critical value, and conclude. While it requires multiple steps and careful calculation, it's a routine application of a core FS1 technique with no conceptual surprises, making it slightly easier than average. |
| Spec | 5.06a Chi-squared: contingency tables |
| Black | Non-black | |
| Men | 69 | 71 |
| Women | 30 | 55 |
Carl believes that the proportions of men and women who own black cars are different. He obtained a random sample of people who each owned exactly one car. The results are summarised in the table below.
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
& Black & Non-black \\
\hline
Men & 69 & 71 \\
\hline
Women & 30 & 55 \\
\hline
\end{tabular}
\end{center}
Test at the 5\% significance level whether Carl's belief is justified. [8]
\hfill \mbox{\textit{OCR FS1 AS 2017 Q3 [8]}}