1 A factory produces bottles of brown sauce and bottles of tomato sauce.
- The content, \(Y\) grams, of a bottle of brown sauce is normally distributed with mean \(\mu _ { Y }\) and variance 4.
A quality control inspection found that the mean content, \(\bar { y }\) grams, of a random sample of 16 bottles of brown sauce was 450 .
Construct a \(95 \%\) confidence interval for \(\mu _ { Y }\).
- The content, \(X\) grams, of a bottle of tomato sauce is normally distributed with mean \(\mu _ { X }\) and variance \(\sigma ^ { 2 }\).
A quality control inspection found that the content, \(x\) grams, of a random sample of 9 bottles of tomato sauce was summarised by
$$\sum x = 4950 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 334$$
- Construct a 90\% confidence interval for \(\mu _ { X }\).
- Holly, the supervisor at the factory, claims that the mean content of a bottle of tomato sauce is 545 grams.
Comment, with a justification, on Holly's claim. State the level of significance on which your conclusion is based.
(3 marks)