The Dome restaurant in Delaware is under new management. While under the previous management, 15% of the customers rated their dining experiences as “unsatisfactory.” The restaurant’s current managers would like to test their belief that this percentage is now lower due to new training procedures. Suppose 75 customers were randomly chosen and asked to rate their dining experiences. Using σ = 0.05, answer the following questions:

a. Explain in your own words how Type I and Type II errors can occur in this hypothesis test.

b. Calculate the probability of a Type II error occurring if the actual proportion of unsatisfied customers is 11%.

c. Calculate the probability of a Type II error occurring if the actual proportion of unsatisfied customers is 6%.