CEE 110 11 PS6 Solutions

# CEE 110 11 PS6 Solutions - UNIVERSITY OF CALIFORNIA LOS...

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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 12-4 PM Frnz 1178 Prof. K. D. Stolzenbach 5732J Boelter Hall, 206-7624 [email protected] Problem Set 6 Solutions _____________________________________________________________________________ 1. a) 1) The parameter of interest is the true mean water temperature, μ . 2) H : μ = 100 3) H 1 : μ < 100 4) 5) Reject H if z < z α where α = 0.05 and z 0.05 = -1.65 6) , σ = 2 7) Because -3.0 < -1.65 reject H . The water temperature is not significantly greater than 100 at α = 0.05. b) P-value = Φ ( − 3.0) = 0.00135 c) n = 1 - Φ (-1.65 + 1.5) = 1 - Φ (-0.15) = 1 - 0.4404 = 0.5596 2. In order to use t statistics in hypothesis testing, we need to assume that the underlying distribution is normal. 1) The parameter of interest is the true mean impact strength, μ . 2) H : μ = 1.0 3) H 1 : μ > 1.0 4) t = 5) Reject H 0 if t > t α ,n-1 where α = 0.05 and t 0.05,19 = 1.729 for n = 20 6) = 1.25 s = 0.25 n = 20 t = 7) Because 4.47 > 1.729 reject the null hypothesis. There is sufficient evidence to conclude that the true mean impact strength is greater than 1.0 ft-lb/in at α = 0.05. The P- value < 0.0005. Exact P-value is 0.000262. 3.3....
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CEE 110 11 PS6 Solutions - UNIVERSITY OF CALIFORNIA LOS...

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