Refer to Exercise 85. Determine if each of the following changes would increase or decrease the power of the test. Explain your answers.

a. Change the significance level to α = 0.10.

b. Take a random sample of 250 potatoes instead of 500 potatoes.

c. The true proportion is p = 0.10 instead of p = 0.11.

Exercise 85.

A company that makes potato chips requires each shipment of potatoes to meet certain quality standards. If the company finds convincing evidence that more than 8% of the potatoes in the shipment have “blemishes,” the truck will be sent back to the supplier to get another load of potatoes. Otherwise, the entire truckload will be used to make potato chips. To make the decision, a supervisor will inspect a random sample of potatoes from the shipment. He will then perform a test of H₀: p = 0.08 versus Ha: p > 0.08 , where p is the true proportion of potatoes with blemishes in a given truckload. The power of the test to detect that p = 0.11, based on a random sample of 500 potatoes and significance level α = 0.05, is 0.764. Interpret this value.