Simulation and Modelling - Old Questions

10. Why Confidence interval is needed in the analysis of simulation output. How can we can we establish a confidence interval?

The confidence interval is the range of possible values for the parameter based on a set of data (e.g. the simulation results.). Confidence interval is needed because:

• A confidence interval displays the probability that a parameter will fall between a pair of values around the mean.
• Confidence intervals measure the degree of uncertainty or certainty in a sampling method.

Confidence intervals are based on the premise that the data being produced by the simulation is represented well by a probability model. Suppose the model is the normally distributed with mean , Variance   and we have a sample of n size then the confidence interval is given by:

In practice, the population variance is usually not known; in this case variance is replaced by the estimate calculated by the formula

This has a student t-distribution, with n – 1 degree of freedom. In terms of estimated variance S², the confidence interval for  is defined by

Here, the quantity  is found on the student t-distribution table.

Example:

Suppose, the daily production time of a product in a factory for 120 days is 5.8 hours and sample standard deviation (S) is 1.6.

Now, confidence interval for 95% confidence level is calculated as;

[t_{119, 0.025} = 1.98]

Hence, the estimates between  can be accepted for 95% confidence interval.