Homework Help is Here – Start Your Trial Now!
Math
Probability
We say that X has a Fisher distribution, denoted by F(n₁, n₂), if K₁/m₁ K₂/n₂ where K₁ ~ X², and K₂ ~ X₂ are two independent r.v.s and the n, 's are degrees of freedom. we have X Let X₁, X₂~ N(ux, ok) and Y₁,..., Ym~ N(μy, o) be two independent samples where the 4 parameters are unknown. We want to test the hypothesis Ho: o = o versus H₁: oo at the (1-a)% confidence level. Answer the following questions:

We say that X has a Fisher distribution, denoted by F(n₁, n₂), if K₁/m₁ K₂/n₂ where K₁ ~ X², and K₂ ~ X₂ are two independent r.v.s and the n, 's are degrees of freedom. we have X Let X₁, X₂~ N(ux, ok) and Y₁,..., Ym~ N(μy, o) be two independent samples where the 4 parameters are unknown. We want to test the hypothesis Ho: o = o versus H₁: oo at the (1-a)% confidence level. Answer the following questions:

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question
We say that X has a Fisher distribution, denoted by F(n₁, n₂), if K₁/m₁ K₂/1₂ where K₁ ~ X₁ and K₂ ~ X₂ are two independent r.v.s and the n; 's are degrees of freedom. Let X₁, X~ N(ux, ok) and Y₁,..., Ym~ N(μy, oz) be two independent samples where the 4 parameters are unknown. We want to test the hypothesis Ho: o = o versus H₁: oo at the (1-a)% confidence level. we have Answer the following questions: (a) If n S = n²x. n - 1 i=1 X = (X-X₂)² and S3 = m 1 - m Σ(Υ; - Ym), j=1 (2) what is the distribution of under Ho and why? (b) If F₁-a (n₁, n₂) denotes the real number for which the area to its left under the F(n1, n₂) density is equal to 1-a, then find a test statistic to test the hypothesis above and write explicitly under which condition we would reject Ho. Note: The support of the F(n₁, n₂) density is (0,00) and the shape of its density is similar to a x² density. In particular, it is not symmetric. (c) Suppose we have the following data, assumed to follow the model above: (xi): 10.62, 10.58, 10.33, 10.72, 10.44, 10.74 (y): 10.50, 10.52, 10.58, 10.62, 10.55, 10.51, 10.53 Test the hypothesis that o = o at the 90% confidence level, using the test from item (b). (Note: F0.05,5,6 = 0.20 and Fo.95,5,6 = 4.39.)
Transcribed Image Text:We say that X has a Fisher distribution, denoted by F(n₁, n₂), if K₁/m₁ K₂/1₂ where K₁ ~ X₁ and K₂ ~ X₂ are two independent r.v.s and the n; 's are degrees of freedom. Let X₁, X~ N(ux, ok) and Y₁,..., Ym~ N(μy, oz) be two independent samples where the 4 parameters are unknown. We want to test the hypothesis Ho: o = o versus H₁: oo at the (1-a)% confidence level. we have Answer the following questions: (a) If n S = n²x. n - 1 i=1 X = (X-X₂)² and S3 = m 1 - m Σ(Υ; - Ym), j=1 (2) what is the distribution of under Ho and why? (b) If F₁-a (n₁, n₂) denotes the real number for which the area to its left under the F(n1, n₂) density is equal to 1-a, then find a test statistic to test the hypothesis above and write explicitly under which condition we would reject Ho. Note: The support of the F(n₁, n₂) density is (0,00) and the shape of its density is similar to a x² density. In particular, it is not symmetric. (c) Suppose we have the following data, assumed to follow the model above: (xi): 10.62, 10.58, 10.33, 10.72, 10.44, 10.74 (y): 10.50, 10.52, 10.58, 10.62, 10.55, 10.51, 10.53 Test the hypothesis that o = o at the 90% confidence level, using the test from item (b). (Note: F0.05,5,6 = 0.20 and Fo.95,5,6 = 4.39.)
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS