- A machine fills bottles with water. The amount of water in each bottle is normally distributed. To check the machine is working properly, a random sample of 12 bottles is selected and the amount of water, in ml, in each bottle is recorded. Unbiased estimates for the mean and variance are
$$\hat { \mu } = 502 \quad s ^ { 2 } = 5.6$$
Stating your hypotheses clearly, test at the 1\% level of significance
- whether or not the mean amount of water in a bottle is more than 500 ml ,
- whether or not the standard deviation of the amount of water in a bottle is less than 3 ml .