CEE 110 10 Final and Solutions

# CEE 110 10 Final and Solutions - UNIVERSITY OF CALIFORNIA...

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Page 1 of 13 UNIVERSITY OF CALIFORNIA, LOS ANGELES Civil and Environmental Engineering Department CEE 110 Introduction to Probability and Statistics for Engineers Spring Quarter 2010 M-W 2-4 PM Young Hall CS24 Prof. K. D. Stolzenbach 5732J Boelter Hall, 206-7624 [email protected] Final Exam (Thursday June 10, 2010) Students are allowed to bring two pages (both sides, approximately 8.5 × 11 inches) of summary notes with them into the examination room. No other material such as textbooks, class notes, or homework is permitted. The exam has five problems with multiple parts. The credit for each part is indicated. Before you start, make sure all pages of your examination are legible. If you have to leave the room for any reason during the exam, please do so quietly without asking. If you have a question during the exam, raise your hand and, if you are in the center of a row, come to the side aisle. Full credit will be given for answers that are worked out correctly, even if the numerically correct answer is not obtained. You may leave your answer in terms of a correct symbolic equation if you like. To obtain credit, be sure to show as much work as possible! There are no long or tricky answers. If you find yourself doing anything long or tricky, stop and reevaluate your approach. Useful formulas and tables are included at the end of the exam.

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Page 2 of 13 1. For each of the following question, indicate the correct answer. Note: you do not have to show your work : 1% a) Disjoint events are: A. always independent B. sometimes independent C. never independent 1% b) In the Total Probability Rule P(A) = P(A | B 1 ) + P(A | B 2 ) + … + P(A | B n ) the events B 1 , B 2 , … B n must be: A. disjoint B. independent C. Bernoulli trials 1% c) The proper way to round off X = 53.4206 ± 0.0164 is: A. X = 53.42 ± 0.02 B. X = 53.421 ± 0.016 C. X = 53.4 ± 0.0 1% d) If a hypothesis test is performed repeatedly on different samples of the same random variable, the probability of rejecting the null hypothesis: A. is the same as the probability of rejection for a single hypothesis test B. is greater than the probability of rejection for a single hypothesis test C. is less than the probability of rejection for a single hypothesis test 1% e) A sample of 100 students entering UCLA as first-year students indicates that the mean age of first-year students is 18.4 years and that the 95% confidence interval for the mean age is 17.7 years to 19.1 years. This result means that: A. The probability that the true mean is between 17.7 years to 19.1 years is 95%. B. The probability that the true mean age is 18.4 years is 95%. C. 95% of confidence intervals computed from a sample of 100 students will contain the true mean. 1% f) A new procedure for analyzing environmental samples is in fact more accurate than other methods. A statistical analysis of data leads to the retention of a null hypothesis that this test is not more accurate than other methods. This is an example of: A. a Type I error B. a Type II error C. the power of the statistical test
Page 3 of 13 Problem 1 continued: 1%

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CEE 110 10 Final and Solutions - UNIVERSITY OF CALIFORNIA...

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