Discussion11%20Solutions - IE 300 / GE 331 Discussion...

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Unformatted text preview: IE 300 / GE 331 Discussion Problem Set 11 8-10 The 99% confidence interval on the mean hole diameter is - 0.005 + 0.005 = 10, = 1.5045, = 0.01, 0.005 = 2.58 a) 0.05,14 = 1.761 b) 0.01,19 = 2.539 c) 0.001,24 = 3.467 8-22 1.4963 1.5127. 8-32 a) The data appear to be approximately normally distributed based on the q-q plot below which exhibits a reasonably straight line. b) = 6, = 16.98, = 0.319, 0.005,5 = 4.032 Note that we should use the t-distribution since the data appear to be approximately normal, variance of the population is unknown, and the sample size is small. The 99% confidence interval on the mean is IE 300 / GE 331 Discussion Problem Set 11 - 0.005,5 + 0.005,5 - 0.01,5 16.455 17.505. c) 0.01,5 = 3.365. The 99% lower confidence bound on the mean is We are 99% confident (NOT PROBABILITY) that the true mean lies within this interval. 16.542 . The lower confidence bound is tighter than the lower bound of the two-sided confidence interval because 0.005,5 > 0.01,5 . a) = 1000 = 0.823, = 1000, /2 = 0.025 = 1.96 8-50 823 The 95% confidence interval on the death rate from lung cancer is b) = 0.03, = 0.823, /2 = 0.025 = 1.96 (1 - ) (1 - ) - /2 + /2 0.7993 0.8467. /2 2 = (1 - ) = 621.79 = 622. 1.968 2 2.5 c) Note that (1 - ) is always less than or equal to 0.25, so /2 2 = (0.25) = 1067.11 = 1068. 8-82 a) = 2.5 = b) = /2 2 The required sample size decreases as the standard deviation decreases. Intuitively, with fixed confidence level and margin of error, it takes a larger sample size for a more variable population. = /2 2 1.966 2 2.5 = = 22.13 = 23 = 39.34 = 40. ...
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This note was uploaded on 05/04/2010 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.

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