Question: Suppose that you wish to test the hypothesis H 0 : 1 = 2 versus H 1 : 1 2

Suppose that you wish to test the hypothesis H₀: μ₁ = μ₂ versus H₁: μ₁ ≠ μ₂, where both variances σ²₁ and σ²₂are known. A total of n₁ + n₂ = N observations can be taken. How should these observations be allocated to the two populations to maximize the probability that H₀ will be rejected if H₁ is true and μ₁ − μ₂ = Δ ≠ 0?

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