Suppose we want to test H o : 1 2 = 2 2 versus H

Suppose we want to test H_o: σ₁² = σ₂²versus H_a:  σ₁² ≠ σ₂². Show that the rejection region given by

where F depends on v₁ = (n₁ - 1)df and v₂ = (n₂ - 1) df, is equivalent to the rejection region given by

where F depends on v₁ numerator df and v₂ denominator df, or

where F* depends on v₂ numerator df and v₁ denominator df. Use the fact (proof omitted) that

where F depends on v₁ numerator df and v₂ denominator df and F* depends on v₂ numerator df and v₁ denominator df.

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Fal2 or F(1-a2)