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# 409Quiz4Dans - = area of the right tail = P Z ≥ 2.00 =...

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STAT 409 Fall 2011 Version D 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 male giraffe heights is normally distributed, and the overall (population) standard deviation of the heights is 0.9 feet. A random sample of n = 9 adult male giraffes had an average height of 15.6 feet. We wish to test H 0 : μ = 15 feet vs. H 1 : μ > 15 feet, where μ is the overall average height of adult male giraffe. a) (3) Find the p-value of this test. Test Statistic: σ is known. 9 9 . 0 15 6 . 15 X Z σ μ 0 - = - = n = 2.00 . Right – tailed test. p-value
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Unformatted text preview: = ( area of the right tail ) = P ( Z ≥ 2.00 ) = 0.0228 . b) (7) If α = 0.035 is used, find ( the significance level ) and ( the power of the test if the true value of the overall average height of adult male giraffe is μ = 15.75 ). Significance level = α = 0.035 . Test Statistic: σ is known. 9 9 . 15 X X Z σ μ-=-= n . Rejection Region: Right - tailed. Reject H if Z > z α = 1.81. 9 9 . 81 . 1 15 X ⋅ + > = 15.543. Power ( μ = 15.75 ) = P ( Reject H | μ = 15.75 ) = P ( X > 15.543 | μ = 15.75 ) = -> 9 9 . 75 . 15 15.543 Z P = P ( Z > – 0.69 ) = 0.7549 ....
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