A machine filles milk bottles, the mean amount of milk per bottle is supposed to be 32 Oz with a standard deviation of 0.06 Oz.The mean amount of milk is normally distributed.Your boss claims that the mean amount of milk per bottle is greater than 32 Oz.To check if the machine is operating properly, 36 filled bottles will be chosen at random.

a.With an alpha = 0.03, you are to test that H0: 32, what should be the rejection criterion be?

b.Find the power of the test if the true mean is 32.03 Oz.

c.Find the probability of a type II error.

d.Explain the type II error and the power of the test you found from above.