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

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