Real estate market cycles are commonly divided into four phases that are based on the rate of change of the demand for and supply of properties:

I-Recovery, II-Expansion, III-Hypersupply, and IV-Recession. The office market cycles of U.S. real estate markets was studied in the Journal of Real Estate Research (July/August 1999). For each of the four market cycles, office rental growth rates (i.e., growth rates for asking rents) were measured for a sample of six different real estate markets. These data (in percentages) are presented in the table below.

a. Specify the null hypothesis for a Kruskal-Wallis test.
b. Rank the 24 measurements in the data set.
c. Find the rank sums and calculate the test statistic.
d. Give the rejection region for the test at a = .05.
e. Is there sufficient evidence to conclude that the distributions of office rental growth rates differ among the four market cycle phases?

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Phase II Phase III Phase I Phase IV 10.5 2.7 -1.0 6.1 1.2 -1.0 6.2 -10.8 2.0 -1.1 -2.3 11.5 9.4 12.2 8.6 10.9 1.1 11.4 3.4 4.2 3.5 4.4 6.2 7.6