Instruction 11-2
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A, B, C, and D). Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$$\begin{array} { | l | c | c | c | c | c | }
\hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR F } \
\hline \text { Neighbbourhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \
\hline \text { Error } & 12 & & & & \
\hline \text { Total } & & & & & \
\hline
\end{array}$$
-Referring to Instruction 11-2,what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?
A) There is not sufficient evidence that the variances are not all the same.
B) There is not sufficient evidence that the variances are all the same.
C) There is sufficient evidence that the variances are not all the same.
D) There is sufficient evidence that the variances are all the same.

Question

Instruction 11-2
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A, B, C, and D). Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR > F } \
\hline \text { Neighbbourhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \
\hline \text { Error } & 12 & & & & \
\hline \text { Total } & & & & & \
\hline
\end{array}$$
-Referring to Instruction 11-2,what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?
A) There is not sufficient evidence that the variances are not all the same.
B) There is not sufficient evidence that the variances are all the same.
C) There is sufficient evidence that the variances are not all the same.
D) There is sufficient evidence that the variances are all the same.

Quizplus · Accepted Answer

The PR > F value of 0.001 is less than the 0.05 significance level, indicating that there is significant evidence of differences between the means of the neighbourhoods, not the variances. Levene's test specifically assesses variances, and a significant result in an ANOVA (which this table represents) does not directly inform about variances. The question seems to confuse the purpose of ANOVA with that of Levene's test. Without specific Levene's test results, we cannot conclude about the homogeneity of variances; thus, the correct interpretation is that there is not sufficient evidence from this information to assess the equality of variances.

Instruction 11-2 a Realtor Wants to Compare the Average Sales-To-Appraisal

Instruction 11-2
a Realtor Wants to Compare the Average Sales-To-Appraisal