Suppose you want to test H0: = 500 against Ha: > 500 using =

Suppose you want to test H0: μ = 500 against Ha: μ > 500 using α = .05. The population in question is normally distributed with standard deviation 100. A random sample of size n = 25 will be used.

a. Sketch the sampling distribution of x, assuming that H0 is true.

b. Find the value of x0, that value of x̅ above which the null hypothesis will be rejected. Indicate the rejection region on your graph of part a. Shade the area above the rejection region and label it a.

c. On your graph of part a, sketch the sampling distribution of x̅ if m = 550. Shade the area under this distribution that corresponds to the probability that ̅ falls in the nonrejection region when μ = 550. Label this area β.

d. Find β.

e. Compute the power of this test for detecting the alternative Ha: μ = 550.