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

Question

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:

Q1: Referring to Scenario 10-17, the among group degrees of freedom is

A) 16

B) 4

C) 3

D) 12

Q2: Referring to Scenario 10-17, the critical value of Levene's test for homogeneity of variances at a 5% level of significance is
A) 3.29

B)3.49

C) 2.48

D) 0.64
Q3: Referring to Scenario 10-17, what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?
A) There is sufficient evidence that the variances are not all the same.

B)There is sufficient evidence that the variances are all the same.

C) There is insufficient evidence that the variances are all the same.

D) There is insufficient evidence that the variances are not all the same.

Source df SS MS F PR>F Neighborhoods 3.1819 1.0606 10.76 0.001 Error 12 Total 4.3644

Explanation / Answer

Q1: As we know,

MS = SS/df

df = SS/ MS

Hence,

Among group degrees of freedom = 3.1819 / 1.0606 = 3

Option C is correct.

Q2: For 3 numerator df and 12 denominator df, F critical value at 5% level of significance:

F = 3.49

Optiob B is correct.

Q3: Since p - value is less than 0.05, we reject the null hypothesis.

Hence,

There is sufficient evidence that the variances are not all the same.

Option A is correct.

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