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Unformatted text preview: UNIVERSITY OF CALIFORNIA, LOS ANGELES
Civil and Environmental Engineering Department
CEE 110 Introduction to Probability and Statistics for Engineers
Spring Quarter 2011
MW 12-2 PM
Franz 1178 Prof. K. D. Stolzenbach
5732J Boelter Hall, 206-7624
[email protected] Problem Set 5 Solutions
1. a) 95% Two-sided CI on the true mean life of a 75-watt light bulb
For α = 0.05, zα/2 = z0.025 = 1.96 , and x = 1014, σ =25 , n=20 b) 95% One-sided CI on the true mean piston ring diameter
For α = 0.05, zα = z0.05 =1.65 and x = 1014, σ =25 , n=20 The lower bound of the one sided confidence interval is higher than the lower bound of the
two-sided confidence interval even though the level of significance is the same. This is
because all of the Type I probability (or α) is in the left tail (or in the lower bound). 2. 95% Confident that the error of estimating the true mean life of a 75-watt light bulb is less
than 5 hours.
For α = 0.05, zα/2 = z0.025 = 1.96 , and σ =25 , E=5 Always round up to the next number, therefore n = 97 3. 99% lower confidence bound on mean Izod impact strength 4. 90% CI on the mean frequency of a beam subjected to loads 5. a) 95% Confidence Interval on the death rate from lung cancer. b) E = 0.03, α = 0.05, zα/2 = z0.025 = 1.96 and = 0.823 as the initial estimate of p,
, n ≅ 622.
c) E = 0.03, α = 0.05, zα/2 = z0.025 = 1.96 at least 95% confident
n ≅ 1068. 6. a) 95% Confidence Interval on the true proportion of helmets showing damage b) c) 7. ...
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