In this study, we calculate confidence intervals for the mean of a normal data and a contaminated normal data. Some robust estimators against outliers are also considered to construct confidence intervals that are more resistant to outliers than the Student t confidence interval. The confidence intervals of these estimators are computed and compared with each other for normal and contaminated normal data to determine which is better. The performance of these confidence intervals is evaluated and compared by calculating the estimated coverage probability, the average width and the standard error by using simulation. Sps t followed by MAD t are recommended at any rate of contamination, while Student t is not preferred at all for contaminated data and the sample mean and the sample standard deviation are not good choices for constructing confidence interval, but highly recommended for normal data without outliers as expected.