Let (y 1 , s 1 2 ) and (y 2 , s 2 2 ) be

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Let (y̅₁, s₁²) and (y̅₂ , s₂²) be the means and variances of two independent random samples of sizes n₁ and n₂, respectively, selected from normal populations with different means, μ₁ and μ₂, but with a common variance, σ².

a. Show that E(y̅₁ - y̅₂) = μ₁ - μ₂.

b. Show that

c. Explain why

is a standard normal random variable.

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Statistics For Engineering And The Sciences

ISBN: 9781498728850

6th Edition

Authors: William M. Mendenhall, Terry L. Sincich

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Question Posted: Apr 15, 2021 07:47 AM

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Let (y 1 , s 1 2 ) and (y 2 , s 2 2 ) be

Question:

V( - y2) = o

Step by Step Answer:

a To show that Ey1 y2 1 2 we can use the linearity of expectation Ey1 y2 Ey1 Ey2 Since y1 and y2 are ...View the full answer

Statistics For Engineering And The Sciences

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