  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.
