Question

For a certain wine, the mean pH (a measure of acidity) is supposed to be 3.32 with a known standard deviation of σ = .14. The quality inspector examines 31 bottles at random to test whether the pH is too low, using a left-tailed test at α = 0.05.

(a) What is the power of this test if the true mean is μ = 3.30?

(b) What is the power of this test if the true mean is μ = 3.28?

(c) What is the power of this test if the true mean is μ = 3.26?

Answer 1

Let denotes the mean pH level.

To test against

At 5% level of significance,

critical value

and rejection region is

a) The power of this test if the true mean is μ = 3.30

ii) The power of this test if the true mean is μ = 3.28

iii) The power of this test if the true mean is μ = 3.26