In a queueing system, it is important to carry out a statistical analysis. When operating a queueing system, monitoring and control of the performance measures of the system are essential to ensure that the system performance is up to design standards. These problems often require statistical analysis of performance measures such as traffic intensity, mean system size, mean queue size, mean sojourn time, and mean waiting time, of which the statistical behaviors reflect the stability of the system. In this work, based on the simulation results, we find a confidence interval for the mean sojourn time in M/G/1 queueing system by bootstrap method and compare five different bootstrap confidence intervals (standard bootstrap, bootstrap-t, bootstrap percentile, Bca, ABC). Simulation resluts show that bootstrap percentile has the best coverage probability and besides that it provides the shortest confidence interval length. We then introduce FEQ method and also a bootstrap method to find confidence intervals for four performance measures W, W_q, L, L_q. We shall show that the FEQ method has a better coverage probability and provides a confidence interval with a shorter average length. Using an asymptotically normal estimator we find a confidence interval for traffic intensity and then we compare this method with the FEQ method and the bootstrap percentile method. We shall show that, among all these methods, the FEQ method provides the best coverage probability and shortest average length. In case traffic intensity is close to one the bootstrap percentile method is preferable method. Finally we introduce asymptotically normal estimator based on the empirical laplace function and find a confidence interval for the sojourn time. We shall show that this confidence interval provides a better coverage probability when the sample size is greater than 100.