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.
Transcribed Image Text:
V( - y2) = o
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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
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Related Book For
Statistics For Engineering And The Sciences
ISBN: 9781498728850
6th Edition
Authors: William M. Mendenhall, Terry L. Sincich
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