CAIE FP2 2010 November — Question 8

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2010
SessionNovember
TopicChi-squared distribution

8 The owner of three driving schools, \(A , B\) and \(C\), wished to assess whether there was an association between passing the driving test and the school attended. He selected a random sample of learner drivers from each of his schools and recorded the numbers of passes and failures at each school. The results that he obtained are shown in the table below.
\multirow{2}{*}{}Driving school attended
\cline { 2 - 4 }\(A\)\(B\)\(C\)
Passes231517
Failures272543
Using a \(\chi ^ { 2 }\)-test and a \(5 \%\) level of significance, test whether there is an association between passing or failing the driving test and the driving school attended.