Five independent replications of the simulation model of a queueing system returned the delays of the...

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Five independent replications of the simulation model of a queueing system returned the delays of the first 20 customers as in the table on the next page. Each replication was initiated with an empty system. (a) The average delay of the first 20 customers is 6.16 according to Replication 3. Is this value a biased or unbiased estimator for the average delay of the first 20 customers (starting with an empty system)? Why? (b) Can we construct a confidence interval for the average delay of the first 20 customers by using the average (1.04) and standard deviation (2.48) of Replication 4 only? Why or why not? (c) The sample mean and standard deviation of the across-replication data (i.c., the averages from independent replications) are 4.63 and 3.00. Can we construct a confidence interval for the average delay of the first 20 customers by using these sample statistics? If yes, explain what the difference is from (b) and calculate the 95% confidence interval. I Customer Replication 1 1 2 3 4 5. 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Average Std. dev. 0 9.7 11.5 30.3 38.1 23.9 19.8 19.4 0 0 0 0 0 0 0 0 1.32 1.3 0 1.05 7.82 12 Replication 2 0 0 0 0 0 0.93 0.59 0 0 6.14 4.83 7.06 2.73 4.74 0 0 0 2.52 4.99 1.91 1.82 241 Replication 3 Replication 4 0 0 5.2 3.96 5.25 7.89 15.3 16.2 0.61 0 0 0 4.18 6.16 6.92 9.36 13.5 10.5 8.44 9.68 6.16 5.24 0 3.36 0 0.81 1.47 0 0 0.03 0 0 0.9 0 0 1.77 1.38 0.21 0 0 0 10.9 1.04 2.48 Replication 5 0 0 0 12.2 16.6 14.2 16.1 16.5 15.2 0 0 7.01 0 2.34 5.11 5.58 5.44 6.57 2.83 0.45 63 6.43 Five independent replications of the simulation model of a queueing system returned the delays of the first 20 customers as in the table on the next page. Each replication was initiated with an empty system. (a) The average delay of the first 20 customers is 6.16 according to Replication 3. Is this value a biased or unbiased estimator for the average delay of the first 20 customers (starting with an empty system)? Why? (b) Can we construct a confidence interval for the average delay of the first 20 customers by using the average (1.04) and standard deviation (2.48) of Replication 4 only? Why or why not? (c) The sample mean and standard deviation of the across-replication data (i.c., the averages from independent replications) are 4.63 and 3.00. Can we construct a confidence interval for the average delay of the first 20 customers by using these sample statistics? If yes, explain what the difference is from (b) and calculate the 95% confidence interval. I Customer Replication 1 1 2 3 4 5. 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Average Std. dev. 0 9.7 11.5 30.3 38.1 23.9 19.8 19.4 0 0 0 0 0 0 0 0 1.32 1.3 0 1.05 7.82 12 Replication 2 0 0 0 0 0 0.93 0.59 0 0 6.14 4.83 7.06 2.73 4.74 0 0 0 2.52 4.99 1.91 1.82 241 Replication 3 Replication 4 0 0 5.2 3.96 5.25 7.89 15.3 16.2 0.61 0 0 0 4.18 6.16 6.92 9.36 13.5 10.5 8.44 9.68 6.16 5.24 0 3.36 0 0.81 1.47 0 0 0.03 0 0 0.9 0 0 1.77 1.38 0.21 0 0 0 10.9 1.04 2.48 Replication 5 0 0 0 12.2 16.6 14.2 16.1 16.5 15.2 0 0 7.01 0 2.34 5.11 5.58 5.44 6.57 2.83 0.45 63 6.43