Working with the Neyman-Pearson Lemma.(a) A sample of size n taken from a normal population with a known variance of σ2 = 9.7969 is used totest H0 : µ = µ0 against H1 : µ = µ1 where µ1 > µ0. Use the Neyman-Pearson Lemma to producea test statistic and the corresponding most powerful critical region at the α level of significance for agiven α.(b) Suppose the sample size is n = 49, H0 : µ = 1 and H1 : µ = 3.5. Find most powerful critical regionat the 1% level of significance for testing H0 against H1. en compute the power of the test. Working with theNeyman-Pearson Lemma.(a) A sample of size n taken from a normal population with a known variance of o² = 9.7969 is used totest Ho: μ = μo against H₁ μ = μ₁ where µ₁ > µo. Use the Neyman-Pearson Lemma to producea test statistic and the corresponding most powerful critical region at the a level of significance for agiven a. Suppose the sample size is n = 49, Ho : μ = 1 and H₁ : μ = 3.5. Find most powerful critical regionat the 1% level of significance for testing Ho against H₁. Then compute the power of the test.

From the given information, σ2=9.7969.

Answered: A sample of size n taken from a normal…

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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Question

Working with the Neyman-Pearson Lemma.

(a) A sample of size n taken from a normal population with a known variance of σ
2 = 9.7969 is used to
test H0 : µ = µ0 against H1 : µ = µ1 where µ1 > µ0. Use the Neyman-Pearson Lemma to produce
a test statistic and the corresponding most powerful critical region at the α level of significance for a
given α.

(b) Suppose the sample size is n = 49, H0 : µ = 1 and H1 : µ = 3.5. Find most powerful critical region
at the 1% level of significance for testing H0 against H1. en compute the power of the test.