Question

1. The null and alternative hypotheses for a one-way ANOVA test are:

*Suppose that in reality the null hypothesis is false. Does this mean that no two of the populations have the same mean? Please explain your answer.

Answer 1

If the null hypothesis for the one way ANOVA is false in reality, then this does not mean that no two of the populations have the same mean. See, the null and alternative hypotheses for a one way ANOVA test are given as below:

Null hypothesis: H₀: All population means are same.

Alternative hypothesis: H_a: At least two population means are different.

‘At least two population means are different’ does not imply that ‘no two of the population means are same’. Two population means would be same, and for another pair, two population means would not be same.

So, we cannot conclude that no two of the populations have the same mean if suppose that in reality the null hypothesis is false.