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) $H _ { 0 } : M _ { 1 } = M _ { 2 } = M _ { 3 } \text { vs. } H _ { 1 } : M _ { 1 } \neq M _ { 2 } \neq M _ { 3 }$
B) $H _ { 0 } : M _ { 1 } = M _ { 2 } = M _ { 3 } \text { vs. } H _ { 1 } : M _ { 1 } \neq M _ { 2 } = M _ { 3 }$
C) $H _ { 0 } : M _ { 1 } = M _ { 2 } = M _ { 3 } \text { vs. } H _ { 1 } : M _ { 1 } = M _ { 2 } \neq M _ { 3 }$
D) $H _ { 0 } : M _ { 1 } = M _ { 2 } = M _ { 3 } \text { vs. } H _ { 1 } : \text { Not all } M _ { j } \text { are equal (where } j = 1,2,3 \text { ) }$

Accepted Answer

The null hypothesis should state that all three models have the same gas mileage population mean, while the alternative hypothesis should state that at least one of them is different. D is the only option that correctly expresses this.

Quiz 12: Chi-Square Tests and Nonparametric Tests