Question: For a one factor completely randomized experiment, there are three groups with the following sample data:

Group 1: Sample mean \(\overline{{{X}_{1}}}\) = 38, sample variance \(S_{1}^{2}\) = 22, sample size n ₁ = 10

Group 2: Sample mean \(\overline{{{X}_{2}}}\) = 42, sample variance \(S_{2}^{2}\) = 15, sample size n ₂ = 10

Group 3: Sample mean \(\overline{{{X}_{3}}}\) = 40, sample variance \(S_{3}^{2}\) = 18, sample size n ₃ = 10

Assuming that all conditions are satisfied for the F test, construct the ANOVA table for this problem. What is your decision at 0.01 level of significance?

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