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.

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Company & Poor & Satisfactory & Good \\
\hline
$P$ & 18 & 43 & 64 \\
\hline
$Q$ & 22 & 22 & 31 \\
\hline
\end{tabular}
\end{center}

(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.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2024 Q5}}