Which of the following is a correctly stated alternative hypothesis for a one-way ANOVA?
A) μ₁ = μ₂ = μ₃
B) μ₁ ≤ μ₂ ≤ μ₃
C) M₁ ≠ M₂ ≠ M₃
D) some μs are not equal.

Question

Quizplus · Accepted Answer

The alternative hypothesis for a one-way ANOVA should state that at least one population mean is different from the others. Therefore, choice D ("some μs are not equal") is the correct alternative hypothesis. Choices A and B simply state that the population means are equal or follow a specific order, which would be the null hypothesis. Choice C uses sample means instead of population means and does not explicitly state that at least one population mean is different from the others, so it is also not an appropriate alternative hypothesis.

Which of the Following Is a Correctly Stated Alternative Hypothesis