A manufacturer of power meters, which are used to regulate energy thresholds of a data communications system, claims that when its production process is operating correctly, only 10% of the power meters will be defective. A vendor has just received a shipment of 25 power meters from the manufacturer. Suppose the vendor wants to test H_O: p = .10 against H_a: p > .10, where p is the true proportion of power meters that are defective. Use Y ≥ 6 as the rejection region.

a. Determine the value of α for this test procedure.

b. Find β if in fact p = .2. What is the power of the test for this value of p?

c. Find β if in fact p = .4. What is the power of the test for this value of p?