409Quiz4Bans - = area of the right tail = P Z ≥ 1.80 =...

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STAT 409 Fall 2011 Version B 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 hippopotamus weights is normally distributed, and the overall (population) standard deviation of the weights is 400 pounds. A random sample of n = 16 adult hippos had an average weight of 5,680 pounds. We wish to test H 0 : μ = 5,500 pounds vs. H 1 : μ > 5,500 pounds, where μ is the overall average weight of adult hippo. a) (3) Find the p-value of this test. Test Statistic: σ is known. 16 400 500 , 5 680 , 5 X Z σ μ 0 - = - = n = 1.80 . Right – tailed test. p-value
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Unformatted text preview: = ( area of the right tail ) = P ( Z ≥ 1.80 ) = 0.0359 . b) (7) If α = 0.075 is used, find ( the significance level ) and ( the power of the test if the true value of the overall average weight of adult hippo is μ = 5,678 ). Significance level = α = 0.075 . Test Statistic: σ is known. 16 400 500 , 5 X X Z σ μ-=-= n . Rejection Region: Right - tailed. Reject H if Z > z α = 1.44. 16 400 44 . 1 500 , 5 X ⋅ + > = 5,644. Power ( μ = 5,678 ) = P ( Reject H | μ = 5,678 ) = P ( X > 5,644 | μ = 5,678 ) = -> 16 400 678 , 5 644 , 5 Z P = P ( Z > – 0.34 ) = 0.6331 ....
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