Let X be N( µ, 100). To test H0 : µ = 80 against H1 : µ > 80, let the critical region be defined by C = {(x1 , x2 , • • • , x25 ) : x > 83}, where x is the sample mean of a random sample of size n = 25 from this distribution.
(a) How is the power function K(µ) defined for this test?
(b) What is the significance level of this test?
(c) What are the values of K(80), K(83), and K(86)?
(d) Sketch the graph of the power function.
(e) What is the p-value corresponding to x = 83.41?