Suppose the Real Estate Commission for the state of Delaware would like to test the hypothesis that the average number of days a home is on the market in New Castle County is 60 days. To test this hypothesis, 32 homes sold during the year were selected and the number of days that the homes were on the market was recorded. Assume the standard deviation for the time on the market is 25 days.

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

b. Using σ = 0.05, calculate the probability of a Type II error occurring if the actual average time for a house on the market is 54 days.

c. Using σ = 0.05, calculate the probability of a Type II error occurring if the actual average time for a house on the market is 78 days.

d. Explain the differences in the results you calculated in parts b and c.