We wish to compare compressive strengths of concrete corresponding to a = 3 different drying methods (treatments). Concrete is mixed in batches that are just large enough to produce three cylinders. Although care is taken to achieve uniformity, we expect some variability among the b = 5 batches used to obtain the following compressive strengths. (There is little reason to suspect interaction, and hence only one observation is taken in each cell.)

(a) Use the 5% significance level and test H_A : α₁ = α₂ = α₃ = 0 against all alternatives.
(b) Use the 5% significance level and test H_B : β₁ = β₂ = β₃ = β₄ = β₅ = 0 against all alternatives.

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Treatment A₁ A₂ A3 Batch B₁ B2 B3 B4 B5 52 47 44 51 42 60 55 49 52 56 48 45 44 43 38