Bootstrapped Pivots for Sample and Population Means and Distribution Functions

In this paper we introduce the concept of bootstrapped pivots for the sample and the population means. This is in contrast to the classical method of constructing bootstrapped confidence intervals for the population mean via estimating the cutoff points via drawing a number of bootstrap sub-samples. We show that this new method leads to constructing asymptotic confidence intervals with significantly smaller error in comparison to both of the traditional t-intervals and the classical bootstrapped confidence intervals. The approach taken in this paper relates naturally to super-population modeling, as well as to estimating empirical and theoretical distributions.