CAIE Further Paper 4 2024 June — Question 3

Exam BoardCAIE
ModuleFurther Paper 4 (Further Paper 4)
Year2024
SessionJune
TopicChi-squared distribution

3 There are three bus companies in a city. The council is investigating whether the buses reliably arrive at their destination on time. The results from random samples of buses from each company are summarised in the following table.
\multirow{2}{*}{}Bus company
\(A\)\(B\)\(C\)Total
\multirow{3}{*}{Arrival}Early22221054
On time305242124
Late28261872
Total8010070250
Test, at the \(5 \%\) significance level, whether the reliability of buses is independent of bus company.