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.
\(9 \quad 7 \quad 8 \quad 9 \quad 6 \quad 11 \quad 7 \quad 9 \quad 8 \quad 9 \quad 8 \quad 10 \quad 7 \quad 9 \quad 9\)
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 \(\mu\). [4]
- Explain whether it was necessary to use the Central Limit theorem in the calculation in part (i). [2]
- 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. [2]