Let 1 , 2 , 3 be, respectively, the means of three normal distributions

Let μ₁, μ₂, μ₃ be, respectively, the means of three normal distributions with a common but unknown variance σ². In order to test, at the α = 5% significance level, the hypothesis H₀ : μ₁ = μ₂ = μ₃ against all possible alternative hypotheses, we take an independent random sample of size 4 from each of these distributions. Determine whether we accept or reject H₀ if the observed values from these three distributions are, respectively,

Transcribed Image Text:

X₁ 5 9 68 X₂ 11 13 10 12 X3 10 6 9 9