CAIE Further Paper 4 2024 June — Question 5

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

5 Two companies, \(P\) and \(Q\), produce a certain type of paint brush. An independent examiner rates the quality of the brushes produced as poor, satisfactory or good. He takes a random sample of brushes from each company. The examiner's ratings are summarised in the table.
CompanyPoorSatisfactoryGood
\(P\)184364
\(Q\)222231
  1. Test, at the \(5 \%\) significance level, whether quality of brushes is independent of company.
  2. Compare the quality of the brushes produced by the two companies.