In forming real estate portfolios, investors typically diversify the geographic locations of their holdings.

While some choose to own properties in a variety of different metropolitan areas, others diversify across submarkets within the same metropolitan region. J.

Rabianski and P. Cheng of Georgia State University investigated the appropriateness of the latter approach as it applics to investing in office properties (Jo~irnul of Real Estate Portfolio Management, Vol. 3,1997). Using the office vacancy rate of a submarket as a proxy for total rate of return lor the ollice submarket, the Submarket Mean Vacancy Rate (%) ...................................................................................

Buckhead 16.85 Downtown 20.73 Midtown 19.75 North Central 16.73 Northeast 16.95 Northwest 16.81 North Lake 20.38 i South 28.26 researchers compared submarkets within several U.S.
metropolitan areas. The table at left presents the mean vacancy rates of the eight office submarkets of Atlanta, Georgia, for a period of nine years. Quarterly vacancy rates were used in calculating the means.

a. Specify the null and alternative hypotheses to usein comparing the mean vacancy rates of the eight office-property submarkets of Atlanta.

b. The researchers reported an ANOVA F statistic of F = 17.54 for the Atlanta data. Conduct the hypothesis test you specified in part

a. Draw the appropriate conclusions in the context of the problem.

c. Givc the approximate p-value for the test you conducted in part b.

d. What assumptions must be met to ensure the validity of the inference you made in part b? Which of these assumptions do you consider the most questionable in this application? Why?