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Sec_8_solutions - CEE 3040 Fall 2008 CEE 304 Section#8...

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CEE 3040 Fall 2008 CEE 304 - Section #8 Example Problems Partial solutions 1. Confidence Intervals for Small Samples: Environmental Engineering Problem Statement: An environmental engineer is studying the concentration of organics in a groundwater source for a rural water supply. Twelve samples yielded a sample mean and sample standard deviation of 152.3 μ g/l and 4.8 μ g/l, respectively. -or- Structural Engineering Problem Statement: The sample average ultimate tensile strength for a sample of 12 high-strength magnetic alloy steel rings used in turbine generators was 152.3 ksi, while the sample standard deviation was 4.8 ksi. a.) Construct a 99% confidence interval for the true mean concentration of organics in this source of water assuming individual observations have a normal distribution. -or- Construct a 99% confidence interval for the true mean tensile strength of such rings assuming individual observations have a normal distribution. Answer: n = 12, x =152.3, 4.8 x s = , α = 1% σ is unknown, n is small, so use t-distribution 2, 1 2, 1 , n n s s CI x t x t n n α α - - = - + 2, 1 0.005,11 3.106 n t t α - = = 4.8 4.8 152.3 3.106 ,152.3 3.106 12 12 CI = - + ( 29 148.0,156.6 CI = b.) Construct a 90% confidence interval for the true mean concentration of organics in this source of water assuming individual observations have a normal distribution -or- Construct a 90% confidence interval for the true mean tensile strength of such rings assuming individual observations have a normal distribution.
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