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Let Y, represent the th 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 S?=(-² (g) For non-zero constants a,'s, what is the distribution of U₂ = a₁Y₁-0₂₂? 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, µ and p2, when o=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.

Let Y, represent the th 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 S?=(-² (g) For non-zero constants a,'s, what is the distribution of U₂ = a₁Y₁-0₂₂? 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, µ and p2, when o=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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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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.
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.
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