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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??

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??

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 6CR
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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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