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Let Y, represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Ya, Yi2,,Yin, of size ni, from the ith population with sample mean Y, and sample variance S?=-1₁-1(Y - Y₁². (a) What is the distribution of Y? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho = o versus Ha: Pio when of is unknown and n; is small. (c) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.

Let Y, represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Ya, Yi2,,Yin, of size ni, from the ith population with sample mean Y, and sample variance S?=-1₁-1(Y - Y₁². (a) What is the distribution of Y? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho = o versus Ha: Pio when of is unknown and n; is small. (c) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.

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
Problem 1P
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Let Y₂ represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Y₁₁, Yi2,,Yin, of size ni, from the ith population with sample mean Y, and sample variance S?=²-1₁-1(Y - Y₁². (a) What is the distribution of Y;? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho: ₁ = o versus Ha Hiio when of is unknown and n; is small. (c) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.
Transcribed Image Text:Let Y₂ represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Y₁₁, Yi2,,Yin, of size ni, from the ith population with sample mean Y, and sample variance S?=²-1₁-1(Y - Y₁². (a) What is the distribution of Y;? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho: ₁ = o versus Ha Hiio when of is unknown and n; is small. (c) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.
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Let Y₂ represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Y₁₁, Yi2,,Yin, of size ni, from the ith population with sample mean Y, and sample variance S?=²-1₁-1(Y - Y₁². (a) What is the distribution of Y;? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho: ₁ = o versus Ha Hiio when of is unknown and n; is small. (c) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.
Transcribed Image Text:Let Y₂ represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Y₁₁, Yi2,,Yin, of size ni, from the ith population with sample mean Y, and sample variance S?=²-1₁-1(Y - Y₁². (a) What is the distribution of Y;? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho: ₁ = o versus Ha Hiio when of is unknown and n; is small. (c) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a.
(d) Define V₁, a function of S², that has a chi-square distribution. (e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument. (f) Find a (1-a) x 100% confidence interval for o
Transcribed Image Text:(d) Define V₁, a function of S², that has a chi-square distribution. (e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument. (f) Find a (1-a) x 100% confidence interval for o
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