4 A doctor wishes to investigate the mean fat content in low-fat burgers. He takes a random sample of 15 burgers and sends them to a laboratory where the mass, in grams, of fat in each burger is determined. The results are as follows.
$$\begin{array} { l l l l l l l l l l l l l l l }
9 & 7 & 8 & 9 & 6 & 11 & 7 & 9 & 8 & 9 & 8 & 10 & 7 & 9 & 9
\end{array}$$
Assume that the mass, in grams, of fat in low-fat burgers is normally distributed with mean \(\mu\) and that the population standard deviation is 1.3 .
- Calculate a \(99 \%\) confidence interval for \(\mu\).
- Explain whether it was necessary to use the Central Limit theorem in the calculation in part (i).
- The manufacturer claims that the mean mass of fat in burgers of this type is 8 g . Use your answer to part (i) to comment on this claim.