4 The volumes of juice in bottles of Apricola are normally distributed. In a random sample of 8 bottles, the volumes of juice, in millilitres, were found to be as follows.
$$\begin{array} { l l l l l l l l }
332 & 334 & 330 & 328 & 331 & 332 & 329 & 333
\end{array}$$
- Find unbiased estimates of the population mean and variance.
A random sample of 50 bottles of Apricola gave unbiased estimates of 331 millilitres and 4.20 millilitres \({ } ^ { 2 }\) for the population mean and variance respectively.
- Use this sample of size 50 to calculate a \(98 \%\) confidence interval for the population mean.
- The manufacturer claims that the mean volume of juice in all bottles is 333 millilitres. State, with a reason, whether your answer to part (ii) supports this claim.