CAIE FP2 2016 June — Question 9

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2016
SessionJune
TopicChi-squared distribution

9 Applicants for a national teacher training course are required to pass a mathematics test. Each year, the applicants are tested in groups of 6 and the number of successful applicants in each group is recorded. The overall proportion of successful applicants has remained constant over the years and is equal to \(60 \%\) of the applicants. The results from 150 randomly chosen groups are shown in the following table.
Number of successful applicants0123456
Number of groups13255138302
Test, at the \(5 \%\) significance level, the goodness of fit of the distribution \(\mathbf { B } ( 6,0.6 )\) for the number of successful applicants in a group.