409Quiz2Bans - 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 B 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 8 adult hippopotamuses had an average weight of 5,600 pounds, with a sample standard deviation of 380 pounds. Assume that the population of adult hippo weights is normally distributed. a) (3) Construct a 95% confidence interval for the overall average weight of adult hippos. σ is unknown The confidence interval: X t s ± α 2 n . n - 1 = 8 - 1 = 7 degrees of freedom α = 0.05 t 0.025 ( 7 ) = 2.365 8 380 365 . 2 600 , 5 ± 5,600 ± 317.74 ( 5,282.26 ; 5,917.74 ) b) (4) Construct a 90% confidence interval for the overall standard deviation of the weights of adult hippos. 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 . 90% confidence level α = 0.10 α 2 = 0.05 . n-1 = 8 -1 = 7 degrees of freedom. 2 05 . 2 2 χ χ = α = 14.07. 2 95 . 2 2 1 χ χ =-= 2.167. ( ) ( ) --⋅ ⋅ 167 . 2 380 1 8 , 07 . 14 380 1 8 2 2 ( 268.03 , 682.97 ) 1. (continued) c) (3) What is the minimum sample size required if we wish to estimate the overall average weight of adult hippos to within 50 pounds with 95% confidence, if the overall standard deviation of the weights is 350 pounds? ε = 50 σ = 350 α = 0.05 z 0.025 = 1.96 2 2 2 50 350 96 . 1 α ε σ z = = ⋅ ⋅ n = 188.2384. Round up. n = 189 ....
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409Quiz2Bans - α-α-χ ⋅ χ ⋅ 2 2 1 2 2 2 2 s s 1 1 n...

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