A machine at Juice Fresh is set to fill fruit juice in 250ml cartons. It is known that when the machine is working properly, the mean amount of juice-filled is 250ml. A supervisor from the quality control department took a random sample of cartons and found that the mean amount of juice-filled was 258ml with a standard deviation of 16ml. Using the 1% Significance level, the supervisor wants to test if the machine is working properly. Assume that the amounts of juice-filled in all such cartons follow the normal distribution. 1. Find the rejection region(s) and calculate the test statistics. [6 marks] 2. Hence, can you conclude that the mean amount of fruit juice filled is different from 250ml? Does the machine need adjustment? [4 marks] (Ctrl)