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Question 1. Use the Neyman-Pearson Lemma for nding the best critical region for testing the null hypothesis ,1: = go against the alternative p = p, > ya when sampling from a normal population with the unknown mean and the variance :1. 2. A process for making steel pipe is under control if the diameter of the pipe has a mean of 3.0000 inches with a standard deviation of 0.0250 inch. To check whether the process is under control, a random sample of size n=30 is taken each day and the null hypothesis ,u = 3.0000 is rejected if E is less than 2.9960 inches or grater than 3.0040. Find the probability of type I error