Let Y₁, Y2, . . ., Yn denote a random sample from a normal distribution with known mean μ and unknown variance σ². Find the most powerful a-level test of H₁: σ² = σ² vs. H₁: σ² = σ², where 3 Show that this test is equivalent to a x2 test. [Hint: Recall that for Z1, Z2 Zn independent standard normal random variables, Zhas a x² distribution with n df.] Is the test from part (b) uniformly most powerful (UMP) for H₁: σ² > σ??

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