CAIE Further Paper 4 2022 November — Question 2

Exam BoardCAIE
ModuleFurther Paper 4 (Further Paper 4)
Year2022
SessionNovember
TopicChi-squared distribution

2 In the colleges in three regions of a particular country, students are given individual targets to achieve. Their performance is measured against their individual target and graded as 'above target', 'on target' or 'below target'. For a random sample of students from each of the three regions, the observed frequencies are summarised in the following table.
\multirow{2}{*}{}Region
ABCTotal
\multirow{3}{*}{Performance}Above target624144147
On target1029495291
Below target564561162
Total220180200600
Test, at the 10\% significance level, whether performance is independent of region.