Let Y, represent the ith normal population with unknown mean , and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size ni, from the ith population with sample mean Y, and sample variance S7=(-)². (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: H = o versus Ha Hi Ho 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 Sf, that has a chi-square distribution.
Let Y, represent the ith normal population with unknown mean , and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size ni, from the ith population with sample mean Y, and sample variance S7=(-)². (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: H = o versus Ha Hi Ho 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 Sf, that has a chi-square distribution.
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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Transcribed Image Text:Let Y, represent the ith normal population with unknown mean , and unknown variance
H
of for i=1,2. Consider independent random samples, Ya, Y2Yin, of size n,, from
the ith population with sample mean Y, and sample variance S7=E(YY)²
(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: 4 = 4o 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.
(d) Define V₁, a function of S7, that has a chi-square distribution.
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