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Cans of black olives are lled by two machines (A and B) in a food processing factory. The distribution of the gross mass is known to be normal with mean 500 g and standard deviation 5.3 g for machine A, and normal with mean 504 g and standard deviation 4.8 g for machine B. A batch of canned black olives have been lled by the same machine, but it is not known which machine was used. As some substandard olives have accidently been used by machine A, it is decided to test Ho: batch is from machine A, against H1: batch is from machine B By weighing a random sample of 6 cans and rejecting Ho if the mean mass exceeds a pre- determined mass of k g. (a) Determine constant k such that the risk of type I error is 5%. What is the corresponding risk of type [I error? (9 marks) (b) Apply and carry out the test for a sample of 6 cans with masses 5] l, 499, 500, 498, 507, 495 g. (3 marks) (0) It is decided to increase the sample size before reaching a nal conclusion. Determine how many more cans are needed to be weighed if the risk of type I error is to remain at 5%, but the risk of type II error is to be reduced to just under 1% 1? What is the decision rule in this case? (8 marks)