Which of the following is a correct formulation for the null hypothesis in one-way ANOVA?
A) $\mu _ { 1 } + \mu _ { 2 } + \mu _ { 3 } = 0$ .
B) $\mu _ { 1 } + \mu _ { 2 } + \mu _ { 3 } \neq 0$ .
C) $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ .
D) $\mu _ { 1 } \neq \mu _ { 2 } \neq \mu _ { 3 }$ .

Question

Quizplus · Accepted Answer

The null hypothesis in one-way ANOVA is always that there is no difference between the means of the groups being compared. This is expressed as $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$, which means that the population means of all three groups are equal. Option A implies that the sum of the population means for all three groups is zero, which is not a valid null hypothesis. Option B implies that at least one of the population means is not equal to the others, which is a statement of the alternative hypothesis. Option D implies that all three population means are different, which is also a statement of the alternative hypothesis.

Which of the Following Is a Correct Formulation for the Null