Refer to Exercise 86. Determine if each of the following changes would increase or decrease the power of the test. Explain your answers.

a. Use a random sample of 30 people instead of 50 people.

b. Try to detect that μ = $85,500 instead of μ=$86,000.

c. Change the significance level to α = 0.10.

Exercise 86.

You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $85,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential site. Based on the mean income of this sample, you will perform a test at the α=0.05 significance level of H₀: μ = $85,000 versus H_a: μ > $85,000, where μ is the true mean income in the population of people who live near the restaurant. The power of the test to detect that μ = $86,000 is 0.64. Interpret this value.