<p> Solutions Chapter 10</p><p>E10.1</p><p>The 95% confidence interval for the results from the ten replications is:</p><p>95% Confidence Interval Mean SD Lower Upper Deviation 202.42 14.864 191.79 213.05 5.25%</p><p>We are 95% confident that the mean daily throughput is in the range 200.23 to 204.61.</p><p>E10.2</p><p>95% confidence interval result when using a batch size of four:</p><p>95% Confidence Interval Mean SD Lower Upper Deviation 186.90 54.52 164.40 209.40 12.04%</p><p>The percentage deviation is quite high (over 12%), which suggests a longer run-length is required.</p><p>E10.3</p><p>Note: exact results will depend on the random numbers generated to create the artificial time- series data.</p><p>The results are shown for a single replication with a warm-up of 60 periods and a run-length of a further 400 periods. The batch size required using Fishman's procedure is 32. The resulting confidence interval is shown below.</p><p>95% Confidence Interval Mean SD Lower Upper Deviation 9.93 0.32 9.72 10.13 2.08%</p><p>1 E10.5</p><p>The table below shows the differences in the means between the scenarios. Note that all the results for scenario 1 are below the results for scenario 2. The sum of variances for the individual results is clearly much greater than the variance of the differences. It would appear, therefore, that the common random numbers are working and that a paired-t confidence interval can be used.</p><p>Scenario 1: Scenario 2: mean daily mean daily Difference Replication t'put t'put (S1-S2) 1 198.2 200.1 -1.94 2 210.5 210.6 -0.06 3 216.6 216.6 -0.01 4 208.2 209.9 -1.67 5 181.8 182.4 -0.63 6 220.8 221.0 -0.25 7 176.4 177.7 -1.31 8 191.7 193.5 -1.76 9 209.3 209.4 -0.15 10 210.7 211.5 -0.78 Mean 202.42 203.28 -0.86 St Dev 14.86 14.49 0.76 Variance 220.94 210.00 0.57</p><p>The paired-t confidence interval is shown below. It is clear that the result for scenario 2 is significantly better, statistically, than for scenario 1. The practical significance of a small increase in throughput should also be considered.</p><p>95% confidence interval for differences Lower interval Upper interval Conclusion -1.40 -0.32 Scenario 1 < Scenario2</p><p>2</p>