  In a two-stage cluster sampling procedure, $n$ random populations are drawn
independently from independent populations and a sub-sample of observations is
taken in each of them. The estimator of the general mean of the observed
variables is asymptotically Gaussian and the asymptotic distributions of
several bootstrap versions of the normalized and studentized statistics are
studied. A weighted population resampling provides a good approximation and its
accuracy depends on the convergence rate of the sample size of the populations.
