The crisis in the real estate market caused the listing prices of homes in areas such as Orlando, Florida, to fall from previous years. A real estate office would like to sample 50 new listings randomly to test the hypothesis that the current listing price average is less than $ 243,000, the average in the previous year. Assume the standard deviation for the price of homes in this market is $ 45,000.

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

b. Using σ = 0.10, calculate the probability of a Type II error occurring if the actual average listing is $ 225,000.

c. Using σ = 0.05, calculate the probability of a Type II error occurring if the actual average listing is $ 225,000.

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