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Let X₁,..., Xn be a random sample from a n(0,0²) population, o² known. An LRT of Ho: 0 = 0o versus H₁ : 000 is a test that rejects Ho if |X - 0o\/(0/√ñ) > 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.

Let X₁,..., Xn be a random sample from a n(0,0²) population, o² known. An LRT of Ho: 0 = 0o versus H₁ : 000 is a test that rejects Ho if |X - 0o\/(0/√ñ) > 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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Let X₁,..., Xn be a random sample from a n(0,0²) population, o² known. An LRT of Ho: 0 = 0o versus H₁: 000 is a test that rejects Ho if X - 0o\/(o/√√n) > 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:Let X₁,..., Xn be a random sample from a n(0,0²) population, o² known. An LRT of Ho: 0 = 0o versus H₁: 000 is a test that rejects Ho if X - 0o\/(o/√√n) > 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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