OCR FS1 AS 2017 Specimen — Question 3 8 marks

Exam BoardOCR
ModuleFS1 AS (Further Statistics 1 AS)
Year2017
SessionSpecimen
Marks8
TopicChi-squared test of independence
TypeStandard 2×2 contingency table
DifficultyStandard +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.
Spec5.06a Chi-squared: contingency tables

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.
BlackNon-black
Men6971
Women3055
Test at the 5\% significance level whether Carl's belief is justified. [8]

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]}}