Question

TABLE 10-16

A realtor wants to compare the average 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:



Referring to Table 10-16, what should be the decision for the Levene’s test for homogeneity of variances at a 5% level of significance?

Group of answer choices

Do not reject the null hypothesis because the p-value is larger than the level of significance.

Reject the null hypothesis because the p-value is larger than the level of significance.

Do not eject the null hypothesis because the p-value is smaller than the level of significance.

Reject the null hypothesis because the p-value is smaller than the level of significance.

Answer 1

The levene's test is performed in the R -software , repective R-code povided along with outputs.

> A=c(1.2, 1.1, 0.9, 0.4)
> B=c(2.5, 2.1, 1.9, 1.6)
> C=c(1.0, 1.5, 1.1, 1.3)
> D=c(0.8, 1.3, 1.1, 0.7)
> x=rep(c("A","B","C","D"),4)
> Y=c(1.2, 1.1, 0.9, 0.4,2.5, 2.1, 1.9, 1.6,1.0, 1.5, 1.1, 1.3,0.8, 1.3, 1.1, 0.7)
> install.packages("car") # if already install this package then kindly aviod this line of code
> library(car)
> leveneTest(Y~x)
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 3   0.3048 0.8214
12   
Warning message:
In leveneTest.default(y = y, group = group, ...) : group coerced to factor.

Conclusion: Here p-value is 0.8214 which is greater than 5% level of significance ,

Therefore correct choice of Answer is

Do not reject the null hypothesis because the p-value is larger than the level of significance.