Suppose that we have been conducting a simulation analysis for a call center system serving different types of calls $($calls can be classified with respect to the corresponding service request or the priority of the calling customer$).$ In order to guarantee a certain customer satisfaction the system consists of multi$-$skilled agents $($an agent can serve a set of different types of calls$).$ A simulation model has been developed for the current system and the average waiting time is chosen as the primary criterion for improving the current system. The estimated value of the expected average waiting time was not satisfactory for the manager and he wants to reduce the expected average waiting time.

After analyzing the reports obtained from the current simulation model, we identified some potential changes $($such as hiring an agent who can serve a certain set of different types of calls$)$ that might be useful to improve the performance measure of interest. Then we propose an alternative configuration representing those changes. After the approval of the manager we modified the current simulation model and developed the model for the system with the proposed modifications. We refer to the initial configuration as the Scenario $1$ and the one with the proposed modifications as the Scenario $2.$ Since we are interested in the rush period, the simulation length of one run was set to $3$ hours $($from $11$:$00$ am to $2$:$00$ pm$).$ After performing certain steps of the simulation analysis, we need to employ an output analysis method to decide whether the improvement by scenario $2$ is statistically significant. $10$ response values $($the values of average waiting time$)$ were collected over $3-$hour periods for each scenario. $($The output data were calculated for $10$ replications of two simulation models$).$ The simulation models obtained the following predictions, for the average waiting time:

$\backslash$table$[[i,1,2,3,4,5,6,7,8,9,10],[\backslash$table$[[Y_i^{(1)}$