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(a) Use this equation to derive a more general expression for a 100(1-a) % CI for μ of which the interval below is a special case. (x-² 1/2 √n' x + ²a/2 x+ 0(X-Z₁₂X+²₁₂) az n √) o O(x-²4₂ √n-1' •₁ X + ² α₁ ² √² VF) 0(X-2₁₂X+²₁₂) n-1 0(X-Z₂X+²₁₂) 0(X-2₂₁X+²₁₂) √) (b) Let a = 0.05 and a₁ = α/4, α₂ = 3a/4. Does this result in a narrower or wider interval than the interval in part (a)? O The interval is narrower. O The interval is wider. O The interval does not change.

(a) Use this equation to derive a more general expression for a 100(1-a) % CI for μ of which the interval below is a special case. (x-² 1/2 √n' x + ²a/2 x+ 0(X-Z₁₂X+²₁₂) az n √) o O(x-²4₂ √n-1' •₁ X + ² α₁ ² √² VF) 0(X-2₁₂X+²₁₂) n-1 0(X-Z₂X+²₁₂) 0(X-2₂₁X+²₁₂) √) (b) Let a = 0.05 and a₁ = α/4, α₂ = 3a/4. Does this result in a narrower or wider interval than the interval in part (a)? O The interval is narrower. O The interval is wider. O The interval does not change.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Let α₁ > 0, α₂ > 0, with α₁ + α₂ = α. Then x-μ P(-²,₂ < X-H <2₁₂) - 1- Р = α. ol√n (a) Use this equation to derive a more general expression for a 100(1-x)% CI for μ of which the interval below is a special case. (x-24/2 √n' X + 0(x-²a₂ 02 za/2 . _, X + ²a ₂ - -/-/-) n √) O(x-28₂√₁X+2₂ VD-1) 0(X-2₁₂X+²₁₁) Zα₁ n-1 0(X-28₂X+2₁₂) Zaq 0(x-Za₂₁ X + Zα₂ F) n-1 (b) Let a = 0.05 and α₁ = α/4, α₂ = 3a/4. Does this result in a narrower or wider interval than the interval in part (a)? The interval is narrower. O The interval is wider. O The interval does not change.
Transcribed Image Text:Let α₁ > 0, α₂ > 0, with α₁ + α₂ = α. Then x-μ P(-²,₂ < X-H <2₁₂) - 1- Р = α. ol√n (a) Use this equation to derive a more general expression for a 100(1-x)% CI for μ of which the interval below is a special case. (x-24/2 √n' X + 0(x-²a₂ 02 za/2 . _, X + ²a ₂ - -/-/-) n √) O(x-28₂√₁X+2₂ VD-1) 0(X-2₁₂X+²₁₁) Zα₁ n-1 0(X-28₂X+2₁₂) Zaq 0(x-Za₂₁ X + Zα₂ F) n-1 (b) Let a = 0.05 and α₁ = α/4, α₂ = 3a/4. Does this result in a narrower or wider interval than the interval in part (a)? The interval is narrower. O The interval is wider. O The interval does not change.
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