Two machines $A$ and $B$ produce the same type of component in a factory. The factory manager wishes to know whether the lengths, $x$ cm, of the components produced by the two machines have the same mean. The manager took a random sample of components from each machine and the results are summarised in the table below.

\includegraphics{figure_4}

The lengths of components produced by the machines can be assumed to follow normal distributions.

\begin{enumerate}[label=(\alph*)]
\item Use a two tail test to show, at the 10\% significance level, that the variances of the lengths of components produced by each machine can be assumed to be equal. [4]

\item Showing your working clearly, find a 95\% confidence interval for $\mu_A - \mu_B$, where $\mu_A$ and $\mu_B$ are the mean lengths of the populations of components produced by machine $A$ and machine $B$ respectively. [7]
\end{enumerate}

There are serious consequences for the production at the factory if the difference in mean lengths of the components produced by the two machines is more than 0.7 cm.

\begin{enumerate}[label=(\alph*)]
\item[(c)] State, giving your reason, whether or not the factory manager should be concerned. [2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S4  Q4 [13]}}