Confidence intervals are important statistical methods used to estimate the location and dispersion parameters of the population. A new robust interval estimator, which is an adjustment of the Student-t confidence interval for estimating population mean based on the decile mean and standard deviation is consider in this research. The efficiency of this proposed interval estimator is evaluated using an extensive Monte-Carlo simulation study. The coverage probabilities and average widths of the proposed interval estimator are compared with some existing widely used interval estimators under normal and contaminated normal distributions. The simulation results show that the proposed interval estimator performs very well in terms of attaining high coverage probability and shorter average width. For illustration purposes, real-life data sets are analyzed which supported the findings obtained from the simulation study to some extent. In summary, our results confirmed that the type of estimator used to construct the confidence interval affects the performance of the interval estimator, and the proposed version of the interval estimator performs better than the other estimators evaluated herein. Consequently, we recommend the new robust conﬁdence interval for the practitioners to be used for estimating of the population mean when the contamination in the data of the distribution is present. The proposed confidence interval of the population mean can be easily calculated by using R program which is providing in this appendix.
Mathematics Subject Classification 62F10; 62F35.