The average size of single-family homes built in the United States is 2,600 square feet (U.S. Census Bureau, 2015). A random sample of 100 new homes sold in California yielded the following size information: x̅ = 2,717 square feet and s = 257 square feet.
a. Assume the average size of U.S. homes is known with certainty. Do the sample data provide sufficient evidence to conclude that the mean size of California homes built exceeds the national average? Test using α = .01.
b. Suppose the actual mean size of new California homes was 2,700 square feet. What is the power of the test in part a to detect this 100-square-foot difference?
c. If the California mean were actually 2,650 square feet, what is the power of the test in part a to detect this 50-square-foot difference?