# 409Quiz4Aans - = area of the right tail = P Z ≥ 1.60 =...

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STAT 409 Fall 2011 Version A Name ANSWERS . Quiz 4 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Assume that the population of adult elephant weights is normally distributed, and the overall (population) standard deviation of the weights is 450 pounds. A random sample of n = 9 adult elephants had an average weight of 12,240 pounds. We wish to test H 0 : μ = 12,000 pounds vs. H 1 : μ > 12,000 pounds, where μ is the overall average weight of adult elephant. a) (3) Find the p-value of this test. Test Statistic: σ is known. 9 450 000 , 12 240 , 12 X Z σ μ 0 - = - = n = 1.60 . Right – tailed test. p-value
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Unformatted text preview: = ( area of the right tail ) = P ( Z ≥ 1.60 ) = 0.0548 . b) (7) If α = 0.015 is used, find ( the significance level ) and ( the power of the test if the true value of the overall average weight of adult elephant is μ = 12,345 ). Significance level = α = 0.015 . Test Statistic: σ is known. 9 450 000 , 12 X X Z σ μ-=-= n . Rejection Region: Right - tailed. Reject H if Z > z α = 2.17. 9 450 17 . 2 000 , 12 X ⋅ + > = 12,325.5. Power ( μ = 12,345 ) = P ( Reject H | μ = 12,345 ) = P ( X > 12,325.5 | μ = 12,345 ) = -> 9 450 345 , 12 12,325.5 Z P = P ( Z > – 0.13 ) = 0.5517 ....
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## This note was uploaded on 11/15/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

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