Real estate market cycles are commonly divided into four phases. Recovery (I), E
ID: 3292804 • Letter: R
Question
Real estate market cycles are commonly divided into four phases. Recovery (I), Expansion (II), Hypersupply (III), and Recession (IV). For each market cycle, office rental growth rates were measured for a sample of five real estate markets. These data (in percentages) are shown in the table. Compare the distributions of the four phases, using an appropriate nonparametric test at alpha = 0.05. What can you infer about the four phases? Specify the null and alternative hypotheses for the appropriate nonparametric test. Choose the correct answer below. H_0: At least two of the four probability distributions are identical. H_a: All of the distributions differ in location. H_0: At least two of the four probability distributions differ in location. H_a: The four probability distributions are identical. H_0: The four probability distributions are identical. H_a: At least two of the four probability distributions differ in location H_0: The four probability distributions are identical. H_a: Exactly two of the four probability distributions differ in location. Provide the test statistic. H = ____ (Round to two decimal places as needed.) Give the rejection region for the test at alpha = 0.05. Choose the correct answer below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.) H > ____ H _____ HExplanation / Answer
The Kruskal Wallis test statistic is as follows:
H=12/n(n+1) sigma i=1 to k Ti^2/ni-3(n+1), where, ni i snumber of measurements in sample i, Ti is rank sum for sample i, where the rank of each measurement is computed according to its' relative magnitude in th etotality of the data for k samples, n=total sample size.
=12/20(20+1)[(41.5)^2/5+(72)^2/5+(56.5)^2/5+(40)^2/5]
=66.85
The rejection region is H>chisquare alpha with k-1 degrees of freedom. Look into the Chi-sqaure table for alpha=0.05, and 3 degrees of freedom [k=4, k-1=3 df, where, k denotes number of groups]
H>7.81
Reject H0 (observed H lie on critical region). There is sufficient evidence.
I Rank1 II Rank2 III Rank3 IV Rank4 22 20 10.4 15 6.1 9.5 11.3 17 1.6 5 10.8 16 12.2 19 4.2 7 6.1 9.5 8.6 12 5.8 8 -10.3 1 -1.5 3.5 7.9 11 9.6 14 -2.4 2 -1.5 3.5 11.8 18 3.7 6 9.3 13 T1=41.5 T2=72 T3=56.5 T4=40Related Questions
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