2. Consider X1, X2, X, iid N(4,0²) where o is known. In this problem we show that among the (1 – a) confidence intervals of the form , P1 + P2 = a, the one with the choice pi = P2 = is the shortest. This explains why the symmetric confidence interval is preferred among all possible choices (unless we want to explicitly construct a one sided confidence interval). a. Without loss of generality, suppose pi < P2. Draw a picture of the standard Normal pdf with z,ı: p2; Za/2: Use it to show that Zp2 < Za/2 < Zpı•

2. Consider X1, X2, X, iid N(4,0²) where o is known. In this problem we show that among the (1 – a) confidence intervals of the form , P1 + P2 = a, the one with the choice pi = P2 = is the shortest. This explains why the symmetric confidence interval is preferred among all possible choices (unless we want to explicitly construct a one sided confidence interval). a. Without loss of generality, suppose pi < P2. Draw a picture of the standard Normal pdf with z,ı: p2; Za/2: Use it to show that Zp2 < Za/2 < Zpı•

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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