6 The contents, in millilitres, of cartons of milk produced at Kream Dairies, can be modelled by a normal distribution with mean 568 and variance \(\sigma ^ { 2 }\). After receiving several complaints from their customers who thought that the average content of the cartons had been reduced, the production manager of Kream Dairies decided to investigate. A random sample of 8 cartons of milk was taken, revealing the following contents, in millilitres. $$\begin{array} { l l l l l l l l } 560 & 568 & 561 & 562 & 564 & 567 & 565 & 563 \end{array}$$ Investigate, at the \(1 \%\) level of significance, whether the average content of cartons of milk is less than 568 millilitres.
(10 marks)