The average size of single family homes in the United States is 2,230 square feet. A

random sample of 100 new homes sold in California yielded the following size information:

x = 2, 347 square feet and s = 257 square feet.

(a) Assume that the average size of U.S. homes is known with certainty. Do the data

provide sufficient evidence to conclude that the mean size of new California homes exceeds

the national average? Use a one-sided test with alpha = .01.

(b) Suppose that the actual mean size of new California homes was 2,330 square feet. Calculate

the probability of the type II error for the test in part (a).

(c) Suppose that the actual mean size of new California homes was 2,280 square feet. Calculate

the probability of the type II error for the test in part (a).