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 ??
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 ??
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3cc4b1e-ed91-4330-9eca-3239f006dbcf%2Fe2fe5522-73ac-45ca-9c93-6fc0c37ba7fe%2Ftkxvcq8_processed.png&w=3840&q=75)
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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