TABLE 12-20
Three new different models of compact SUVs have just arrived at the market. You are interested in comparing the gas mileage performance of all three models to see if they are the same. A partial computer output for twelve compact SUVs of each model is given below:

You are told that the gas mileage population distributions for all three models are not normally distributed.
-Referring to Table 12-20, what should be the null and alternative hypotheses of the test?
A) H₀: M₁ = M₂ = M₃ vs. H₁: M₁ ≠ M₂ ≠ M₃
B) H₀: M₁ = M₂ = M₃ vs. H₁: M₁ ≠ M₂ = M₃
C) H₀: M₁ = M₂ = M₃ vs. H₁: M₁ = M₂ ≠ M₃
D) H₀: M₁ = M₂ = M₃ vs. H₁: Not all Mⱼ are equal (where j = 1, 2, 3)

Question

TABLE 12-20
Three new different models of compact SUVs have just arrived at the market. You are interested in comparing the gas mileage performance of all three models to see if they are the same. A partial computer output for twelve compact SUVs of each model is given below:
  
You are told that the gas mileage population distributions for all three models are not normally distributed.
-Referring to Table 12-20, what should be the null and alternative hypotheses of the test?
A) H₀: M₁ = M₂ = M₃ vs. H₁: M₁ ≠ M₂ ≠ M₃ 
B) H₀: M₁ = M₂ = M₃ vs. H₁: M₁ ≠ M₂ = M₃ 
C) H₀: M₁ = M₂ = M₃ vs. H₁: M₁ = M₂ ≠ M₃ 
D) H₀: M₁ = M₂ = M₃ vs. H₁: Not all Mⱼ are equal (where j = 1, 2, 3)

Quizplus · Accepted Answer

Since the population distributions for gas mileage for all three models are not normally distributed, we cannot perform an ANOVA test. Therefore, we need to conduct a nonparametric test, specifically the Kruskal-Wallis test, which tests whether there is a significant difference in the location of the gas mileage population distributions across all three models. The null hypothesis for the Kruskal-Wallis test is that all three population distributions are equal, while the alternative hypothesis is that not all of them are equal. Therefore, choice D is the correct hypothesis statement for this test.

TABLE 12-20 Three New Different Models of Compact SUVs Have Just Arrived