- 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).
$$\begin{array} { l l l l l l }
512 & 503 & 514 & 506 & 509 & 515
\end{array}$$
The weights, \(y\) grams, of the contents of an independent random sample of 5 new style boxes gave
$$\bar { y } = 504.8 \text { and } s _ { y } = 3.420$$
- 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.
- 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.
- With reference to your confidence interval comment on the manufacturer's claim.