Answered: 8.3.11 Let X₁,..., Xn and Y₁,..., Ym be… | bartleby

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Question

8.3.11 Let X₁,..., Xn and Y₁,..., Ym be independent random samples from the
distributions N(01,03) and N(02,04), respectively.
(a) Show that the likelihood ratio for testing Ho : 0₁ = 02, 03 = 04 against all
alternatives is given by
n/2
m/2
n
m
Σ(x - 7)2/n
Σ(yi - g)3/m
Σ
1
m
(x₁ −u)² + Σ(yi - u)²
Σ
20) 27/01
where u = (na+my)/(n+m).
(n+m)/2
(m + n)
(n)}"

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