9231 P41 - Jun 2024 - Q5 - 8 marks
6664
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.
Company | Poor | Satisfactory | Good |
|---|---|---|---|
\(P\) | 18 | 43 | 64 |
\(Q\) | 22 | 22 | 31 |
(a) Test, at the \(5 \%\) significance level, whether quality of brushes is independent of company.
(b) Compare the quality of the brushes produced by the two companies.
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