A realtor wants to compare the average sales-to-appraisal ratios of residential

Question

A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). For properties are randomly selected from each neighborhood and the ratios for each, as shown below. A: 1, 2, 1.1, 0.9, 0.4 B. 2.5, 2.1, 1.9, 1.6 D: 1.0, 1.5, 1.1, 1.3 D: 0.8, 1.3, 1.1, 0.7 Interpret the results of the analysis summarized in the following table: Referring to table 11-3, a) at the 0.05 level of significance, the mean radios for the 4 neighborhoods are not all the same. b) at the 0.01 level of significance, the mean ratios for the 4 neighborhoods are all the same. c) at the 0.10 level of significance, the mean ratios for the 4 neighborhoods are not significantly different. d) at the 0.05 level of significance, the mean ratios for the 4 neighborhoods are not significantly different from 0.

Explanation / Answer

degree of freedom for neighbourhood will be given by,

dfneighbourhoods = 4 - 1 = 3

Total degree of freedom would be given by,

dftotal = dfneighbourhoods +dferror = 3+12 = 15

The sum of squares for error would be given by,

SSerror = SStotal - SSneighbourhoods = 4.3644 - 3.1819 = 1.1825

The mean square for error would be given by,

MSerror = SSerror /dferror = 1.1825/12 = 0.0985

Since the P-value (0.001) is very low we will reject the null hypothesis. Therefore the mean for the 4 groups is not equal.

24.

The correct option would be ,

a) at the 0.05 level of significance , mean ratios for the 4 neighbouroods are not all the same.

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