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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Let Y₁, Y₂, Yn denote a random sample from a normal distribution with
known mean and unknown variance σ².
μ
4 Find the most powerful a-level test of Ho: σ² = σ² vs. H₁: σ² = σ2, where
σ² > 0.
Show that this test is equivalent to a x2 test. [Hint: Recall that for Z1, Z2,
"
Zn independent standard normal random variables,
distribution with n df.]
Zhas a x²
2. Is the test from part (b) uniformly most powerful (UMP) for Hå: σ² > σ²?
Transcribed Image Text:Let Y₁, Y₂, Yn denote a random sample from a normal distribution with known mean and unknown variance σ². μ 4 Find the most powerful a-level test of Ho: σ² = σ² vs. H₁: σ² = σ2, where σ² > 0. Show that this test is equivalent to a x2 test. [Hint: Recall that for Z1, Z2, " Zn independent standard normal random variables, distribution with n df.] Zhas a x² 2. Is the test from part (b) uniformly most powerful (UMP) for Hå: σ² > σ²?
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