PrelimExam2010

# PrelimExam2010 - Prelim Exam Solutions 2010 1. (25 points)...

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Prelim Exam Solutions 2010 1 1. (25 points) Hypothesis Testing Assume you are implementing SA and GA to maximize an expensive cost function. You run 10 trials of 200 iterations and the best solutions, the means and the standard deviations are given below: Trial SA GA 1 108.71 79.08 2 95.22 88.33 3 105.15 90.89 4 108.77 77.50 5 96.97 83.53 6 103.42 82.40 7 78.22 77.64 8 95.38 80.43 9 90.24 67.04 10 96.70 84.33 Mean 97.88 81.12 Std 8.83 6.27 (a) Which hypothesis test (2-sample t-test or paired t-test) would you perform on the data and why? (b) State your null and alternative hypothesis (c) What is your test statistic? (d) Based on the table given below, what is your rejection region for α = 0.05? α 0.1 0.05 0.025 0.01 0.005 0.001 0.0005 t α 1.330 1.734 2.101 2.552 2.878 3.610 3.922 Z α 1.282 1.645 1.960 2.326 2.576 3.090 3.291 (e) What is your conclusion from the hypothesis test, i.e. does the hypothesis test tell you one algorithm performs better than the other or does it tell you that there is no statistical evidence that they are different? 2. (13 points) Short answer questions: (a) Four algorithms are compared using an empirical CDF shown below.

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Prelim Exam Solutions 2010 2 (i) Which algorithm performs best if we wish to maximize the objective function? Give one reason why you think so. (ii) For each algorithm, indicate if it is stochastically dominated by any other algorithm and indicate which algorithms stochastically dominate it. 3.
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## This note was uploaded on 11/29/2011 for the course ORIE 5140 taught by Professor Shoemaker during the Fall '11 term at Cornell University (Engineering School).

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PrelimExam2010 - Prelim Exam Solutions 2010 1. (25 points)...

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