409Quiz2Aans - α-α-χ ⋅ χ ⋅ 2 2 1 2 2 2 2 s s 1 1 n...

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STAT 409 Fall 2011 Version A Name ANSWERS . Quiz 5 (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. A sample of 6 adult elephants had an average weight of 12,200 pounds, with a sample standard deviation of 420 pounds. Assume that the population of adult elephant weights is normally distributed. a) (3) Construct a 90% confidence interval for the overall average weight of adult elephants. σ is unknown The confidence interval: X t s ± α 2 n . n - 1 = 6 - 1 = 5 degrees of freedom α = 0.10 t 0.05 ( 5 ) = 2.015 6 420 015 . 2 200 , 12 ± 12,200 ± 345.5 ( 11,854.5 ; 12,545.5 ) b) (4) Construct a 95% confidence interval for the overall standard deviation of the weights of adult elephants. The confidence interval : ( ) ( )
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Unformatted text preview: α-α--χ ⋅ χ ⋅ 2 2 1 2 2 2 2 s s 1 , 1 n n . 95% confidence level α = 0.05 α 2 = 0.025 . n-1 = 6 -1 = 5 degrees of freedom. 2 025 2 2 . χ χ = α = 12.83. 2 975 2 2 1 . χ χ = α-= 0.831. ( ) ( ) --⋅ ⋅ 831 . 420 1 6 , 83 . 12 420 1 6 2 2 ( 262.193 , 1030.229 ) 1. (continued) c) (3) What is the minimum sample size required if we wish to estimate the overall average weight of adult elephants to within 100 pounds with 90% confidence, if the overall standard deviation of the weights is 400 pounds? ε = 100 σ = 400 α = 0.10 z 0.05 = 1.645 2 2 2 100 400 645 . 1 α ε σ z = = ⋅ ⋅ n = 43.2964. Round up. n = 44 ....
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