The weights of the contents of breakfast cereal boxes are normally distributed. A manufacturer changes the style of the boxes but claims that the weight of the contents remains the same.
A random sample of 6 old style boxes had contents with the following weights (in grams).

512, 503, 514, 506, 509, 515

The weights, $y$ grams, of the contents of an independent random sample of 5 new style boxes gave

$$\bar{y} = 504.8 \text{ and } s_y = 3.420$$

\begin{enumerate}[label=(\alph*)]
\item Use a two-tail test to show, at the 10\% level of significance, that the variances of the weights of the contents of the old and new style boxes can be assumed to be equal. State your hypotheses clearly.
[5]

\item Showing your working clearly, find a 90\% confidence interval for $\mu_x - \mu_y$ where $\mu_x$ and $\mu_y$ are the mean weights of the contents of old and new style boxes respectively.
[7]

\item With reference to your confidence interval comment on the manufacturer's claim.
[2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S4  Q5 [14]}}