6. A butter packing machine cuts butter into blocks. The weight of a block of butter is normally distributed with a mean weight of 250 g and a standard deviation of 4 g . A random sample of 15 blocks is taken to monitor any change in the mean weight of the blocks of butter.
- Find the critical region of a suitable test using a \(2 \%\) level of significance.
(3) - Assuming the mean weight of a block of butter has increased to 254 g , find the probability of a Type II error.