In a one-way ANOVA with three groups, the null hypothesis states?

Question

Choose one of the following:

 

A) at least two of the means differ

B) μ₁=μ₂=μ₃

C) μ1≥ μ₂ and μ₃

D) there exists in the set of i and j at least one value for which μ_i and μ_j are not equal

E) all of the means differ

Answer 1

Your null hypothesis is always your hypothesis of equality. Of the five choices, the only one suggesting equality is:

 

B

Answer 2

Answer (B)

 

ANOVA provides a simultaneous test of of the null hypothesis that the group population means are equals for three or more groups. The alternative hypothesis is that at least one group mean (population) is different from the rest. The rejection region (in favor of the alternative hypothesis) is that the calculated F ratio is "too high" (higher than the critical value of F at a prescribed level of significance).