Question

If there are three groups, null hypothesis for the one-way ANOVA is

a) H₀:μ₁ = μ₂ > μ₃

b) H₀:Μ₁ = Μ₂ = μ₃

c) H₀:μ₁ = μ₂ = μ₃

d) H₀:Μ₁ = Μ₂ = Μ₃

Answer 1

Answer : c) H0:μ1 = μ2 = μ3

Explanation: In one-way ANOVA, we test the null hypothesis that Ho: There is no significant difference between group means. In other words, group means are all equal.

In example in hand, we have three groups. Hence our null hypothesis will be, group means of three groups are all equal. Hence option c) H0:μ1 = μ2 = μ3 is correct.

Now consider other options. In option a, there is greater than condition μ1 = μ2 > μ3. Hence option a is incorrect. In option b and d, we are talking about M, which is not group mean (population mean). Hence option b & d are incorrect.