Suppose we have a random sample of size 25 from a normal population with an unknown mean m and a standard deviation of 4. We wish to test the hypothesis H0:m=10 versus Ha: m > 10. Let the rejection region be defined by: reject H0 if the sample mean X > 11:2:
(a) Find a.
(b) Find b for Ha: m = 11.
(c) What should the sample size be if a = 0.01 and b = 0.2?