Question 4 (15+5+5+5 = 30 points) - Consider the ranking and selection (R&S) procedure discussed in class, under the more realistic assumption that the variances of the normally distributed populations N(u, o) studied could be different. Specifically, consider the following distributions: N(11, 1.2), N(11, 1.3), N(12, 1.3), N(13, 1.4), and N(13.5, 1.5). Apply R&S repeatedly 20 times, with 30 simulated outcomes in each run, and record your results. 4.1 Based on the results, draw your conclusion: are the selection and ranking procedures still working adequately or not? 4.2 What is the expected effect of changing the differences of the mean values? 4.3 What is the expected effect of changing the variances to smaller or larger values? 4.4 What would happen if you increased the number of repetitions from 30 to say 1000, in each simulation sequence? Population 1 650 Population 2 660 Population 3 675 Population 4 690 Population 5 700 Mean Standard deviation 25 25 25 25 25 Random Observations 1 678.547 679.436 601.306 659.393 2 673.068 655.327 3 660.789 679.388 646.362 664.753 654.210 4 704.265 675.969 694.900 692.249 644.648 605.536 630.186 725.413 683.431 709.587 742.701 714.675 695.825 692.171 755.539 742.790 669.936 699.292 731.136 5 6 7 655.558 641.902 663.446 8 646.145 669.941 696.746 647.439 688.015 672.347 671.793 666.084 663.873 9 667.948 10 11 630.128 633.701 690.162 653.023 685.637 704.282 687.953 694.561 696.330 718.876 678.489 706.701 706.891 709.076 652.635 655.803 Sample average 675.363 Press F9 to generate another random sample instance, and observe the correct or incorrect selection of the best population n=2 n= 3 n=4 n= 5 delta = 20 alpha = 0.90 N(delta, alpha) 11 0.95 0.90 0.75 2.3262 1.8124 0.9539 2.7101 2.2302 1.4338 2.9162 2.4516 1.6822 3.0552 2.5997 1.8463 Question 4 (15+5+5+5 = 30 points) - Consider the ranking and selection (R&S) procedure discussed in class, under the more realistic assumption that the variances of the normally distributed populations N(u, o) studied could be different. Specifically, consider the following distributions: N(11, 1.2), N(11, 1.3), N(12, 1.3), N(13, 1.4), and N(13.5, 1.5). Apply R&S repeatedly 20 times, with 30 simulated outcomes in each run, and record your results. 4.1 Based on the results, draw your conclusion: are the selection and ranking procedures still working adequately or not? 4.2 What is the expected effect of changing the differences of the mean values? 4.3 What is the expected effect of changing the variances to smaller or larger values? 4.4 What would happen if you increased the number of repetitions from 30 to say 1000, in each simulation sequence? Population 1 650 Population 2 660 Population 3 675 Population 4 690 Population 5 700 Mean Standard deviation 25 25 25 25 25 Random Observations 1 678.547 679.436 601.306 659.393 2 673.068 655.327 3 660.789 679.388 646.362 664.753 654.210 4 704.265 675.969 694.900 692.249 644.648 605.536 630.186 725.413 683.431 709.587 742.701 714.675 695.825 692.171 755.539 742.790 669.936 699.292 731.136 5 6 7 655.558 641.902 663.446 8 646.145 669.941 696.746 647.439 688.015 672.347 671.793 666.084 663.873 9 667.948 10 11 630.128 633.701 690.162 653.023 685.637 704.282 687.953 694.561 696.330 718.876 678.489 706.701 706.891 709.076 652.635 655.803 Sample average 675.363 Press F9 to generate another random sample instance, and observe the correct or incorrect selection of the best population n=2 n= 3 n=4 n= 5 delta = 20 alpha = 0.90 N(delta, alpha) 11 0.95 0.90 0.75 2.3262 1.8124 0.9539 2.7101 2.2302 1.4338 2.9162 2.4516 1.6822 3.0552 2.5997 1.8463