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?
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?
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%2F151fe960-fd98-42a8-aa43-e48c578092ab%2Fh4low7k_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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