
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text: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 n,, from
the ith population with sample mean Y, and sample variance S?=₁1(Yu - Y.².
(g) For non-zero constants a,'s, what is the distribution of U₂ = a₁Y₁-a₂Y₂? State all
the relevant parameters of the distribution.
(h) Find the standard error of U₂ in part (g), assuming that of = o2 = 0².
(i) Discuss how the distribution of Y₁ - ₂ can be used to test the equality of the two
population means, #, and p2, when of=o=o² is known.
(j) Define appropriate rejection regions, in terms of Y₁ - ₂, for testing Ho: #₁ = ₂
against a two-sided alternative hypothesis at the a level of significance.
Expert Solution

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Step 1: Write the given information.
For the first variable :
The sample size is .
The sample mean is .
The sample variance is .
For the second variable :
The sample size is .
The sample mean is .
The sample variance is .
The samples are independent.
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