7 A factory produces 3-litre bottles of mineral water. The volume of water in a bottle has previously had a mean value of 3020 millilitres. Following a stoppage for maintenance, the volume of water, \(x\) millilitres, in each of a random sample of 100 bottles is measured and the following data obtained, where \(y = x - 3000\).
$$\sum y = 1847.0 \quad \sum ( y - \bar { y } ) ^ { 2 } = 6336.00$$
- Carry out a hypothesis test, at the \(5 \%\) significance level, to investigate whether the mean volume of water in a bottle has changed.
(8 marks) - Subsequent measurements establish that the mean volume of water in a bottle produced by the factory after the stoppage is 3020 millilitres. State whether a Type I error, a Type II error or no error was made when carrying out the test in part (a).
(l mark)