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3) Let X1, X2,..., X, be i.i.d. N(01,02). Show that the likelihood ratio principle for testing Ho : 02 = 6, specified, and 0, unspecified vs. H. : 02 # 62, 01 unspecified, leads to a test that rejects when ("; – #)² < ¢1 or D(; – 1)² > c2, i=1

3) Let X1, X2,..., X, be i.i.d. N(01,02). Show that the likelihood ratio principle for testing Ho : 02 = 6, specified, and 0, unspecified vs. H. : 02 # 62, 01 unspecified, leads to a test that rejects when ("; – #)² < ¢1 or D(; – 1)² > c2, i=1

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 35E
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3) Let X1, X2, .., X, be i.i.d. N(@1,02). Show that the likelihood ratio principle for testing Ho : 02 = 6, specified, and 0, unspecified vs. H. : O2 # O2, 01 unspecified, leads to a test that rejects when %3D (T; – T)² < ¢1 or #; - 7)² > c2; i=1 i=1 where ci < c2 are selected appropriately.
Transcribed Image Text:3) Let X1, X2, .., X, be i.i.d. N(@1,02). Show that the likelihood ratio principle for testing Ho : 02 = 6, specified, and 0, unspecified vs. H. : O2 # O2, 01 unspecified, leads to a test that rejects when %3D (T; – T)² < ¢1 or #; - 7)² > c2; i=1 i=1 where ci < c2 are selected appropriately.
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