TABLE 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table:
Source df SS MS F PR F
Neighborhoods 3.1819 1.0606 10.76 0.001
Error 12
Total 4.3644
-Referring to Table 11-2, the null hypothesis for Levene's test for homogeneity of variances is
A) H₀: μA = μB = μC = μD.
B) H₀: MA = MB = MC = MD.
D) H₀: πA = πB = πC = πD.

Question

TABLE 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table:
Source df SS MS F PR > F
Neighborhoods 3.1819 1.0606 10.76 0.001
Error 12
Total 4.3644
-Referring to Table 11-2, the null hypothesis for Levene's test for homogeneity of variances is
A) H₀: μA = μB = μC = μD. 
B) H₀: MA = MB = MC = MD. 
D) H₀: πA = πB = πC = πD.

Quizplus · Accepted Answer

Levene's test compares the variances of the groups, so the null hypothesis states that the variances of the four neighborhoods are equal. Therefore, H₀: σ²A = σ²B = σ²C = σ²D can be rewritten as H₀: πA = πB = πC = πD, where π represents population variance. Choice A is the null hypothesis for a one-way ANOVA comparing the means of the four groups. Choice B is an incorrect statement since comparing means is not the purpose of Levene's test.

TABLE 11-2 a Realtor Wants to Compare the Mean Sales-To-Appraisal Ratios of Ratios