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CEE 110 11 PS7 Solutions

# CEE 110 11 PS7 Solutions - UNIVERSITY OF CALIFORNIA LOS...

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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 Problem Set 7 Solutions _____________________________________________________________________________ 1. Expected Frequency is found by using the Poisson distribution Value 0 1 2 3 4 Observed Frequency 24 30 31 11 4 Expected Frequency 30.12 36.14 21.69 8.67 2.60 Since value 4 has an expected frequency less than 3, combine this category with the previous category: Value 0 1 2 3-4 Observed Frequency 24 30 31 15 Expected Frequency 30.12 36.14 21.69 11.28 The degrees of freedom are k p 1 = 4 0 1 = 3 a) 1) The variable of interest is the form of the distribution for X. 2) H 0 : The form of the distribution is Poisson 3) H 1 : The form of the distribution is not Poisson 4) The test statistic is 5) Reject H 0 if for α = 0.05 6) χ 0 2 = 24 30.12 ( ) 2 30.12 + 30 36.14 ( ) 2 36.14 + 31 21.69 ( ) 2 21.69 + 15 11.28 ( ) 2 11.67 = 7.52 7) Because 7.52 < 7.81 fail to reject H 0 . We are unable to reject the null hypothesis that the distribution of X is Poisson.

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CEE 110 11 PS7 Solutions - UNIVERSITY OF CALIFORNIA LOS...

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