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8.18 Let X₁,..., X₂, be a random sample from a n(0,0²) population, ² known. An LRT of Ho: 0 = 0o versus H₁: 000 is a test that rejects Ho if X-00/(0/√) > c. (a) Find an expression, in terms of standard normal probabilities, for the power func- tion of this test. (b) The experimenter desires a Type I Error probability of .05 and a maximum Type II Error probability of .25 at 0=0o+o. Find values of n and c that will achieve this.

8.18 Let X₁,..., X₂, be a random sample from a n(0,0²) population, ² known. An LRT of Ho: 0 = 0o versus H₁: 000 is a test that rejects Ho if X-00/(0/√) > c. (a) Find an expression, in terms of standard normal probabilities, for the power func- tion of this test. (b) The experimenter desires a Type I Error probability of .05 and a maximum Type II Error probability of .25 at 0=0o+o. Find values of n and c that will achieve this.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Textbook: Statistical Inference Casella and Berger

8.18 Let X₁,..., X₂, be a random sample from a n(0,0²) population, ² known. An LRT of Ho: 0 = 0o versus H₁: 000 is a test that rejects Ho if X-00/(0/√) > c. (a) Find an expression, in terms of standard normal probabilities, for the power func- tion of this test. (b) The experimenter desires a Type I Error probability of .05 and a maximum Type II Error probability of .25 at 0=0o+o. Find values of n and c that will achieve this.
Transcribed Image Text:8.18 Let X₁,..., X₂, be a random sample from a n(0,0²) population, ² known. An LRT of Ho: 0 = 0o versus H₁: 000 is a test that rejects Ho if X-00/(0/√) > c. (a) Find an expression, in terms of standard normal probabilities, for the power func- tion of this test. (b) The experimenter desires a Type I Error probability of .05 and a maximum Type II Error probability of .25 at 0=0o+o. Find values of n and c that will achieve this.
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