In: Statistics and Probability
Let X be from a normal distribution with mean u and varince 4.
We would like to test the null hypothesis H0: u=10 against the
alternative hypothesis H1: u>10. Let the rejection region be
defined by C={(x1,x2,...,x9): X.bar>=11.5}, where X.bar is the
sample mean of a random sample of size 9 from this
distribution.
(a) what's the significance level of this test?
(b) Define the power function for this test.
(c) what are the power when u=11, 11.5 and 12?