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# HW 9 - STAT 400 Homework#9 due Friday November 4 by 3:00...

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STAT 400 Homework #9 Fall 2011 ( due Friday, November 4, by 3:00 p.m. ) 1. A store sells "16-ounce" boxes of Captain Crisp cereal. A random sample of 9 boxes was taken and weighed. The results were the following (in ounces): 15.5 16.2 16.1 15.8 15.6 16.0 15.8 15.9 16.2 Assume the weight of cereal in a box is normally distributed. a) Compute the sample mean x and the sample standard deviation s . 9 1 . 143 = = n x x i = 15.9 . ( ) ( ) 8 5 . 0 8 9 1 . 143 79 . 2275 1 2 2 2 2 = = = - - - n n x x s i i = 0.0625. OR 1 ) ( 2 2 - - = n x x s i = 8 5 . 0 = 0.0625. 0625 . 0 2 = = s s = 0.25 . b) Construct a 95% confidence interval for the overall average weight of boxes of Captain Crisp cereal. σ is unknown. n = 9 - small. The confidence interval : X t s ± α 2 n . α = 0.05 α 2 = 0.025 . number of degrees of freedom = n - 1 = 9 - 1 = 8. t α 2 = 2.306. 9 25 . 0 306 . 2 9 . 15 ± 15.9 ± 0.192 ( 15.708 , 16.092 )

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c) Construct a 95% confidence upper bound for the overall average weight of boxes of Captain Crisp cereal. + n s t X , 0 α 8 degrees of freedom t 0.05 = 1.860. + 9 25 . 0 1.860 15.9 , 0 ( 0 , 16.055 ) d) Construct a 90% confidence lower bound for the overall average weight of boxes of Captain Crisp cereal. - , X s t n 8 degrees of freedom t 0.10 = 1.397. - , 9 25 . 0
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HW 9 - STAT 400 Homework#9 due Friday November 4 by 3:00...

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