  We study nonparametric estimation of the distribution function (DF) of a
continuous random variable based on a ranked set sampling design using the
exponentially tilted (ET) empirical likelihood method. We propose ET estimators
of the DF and use them to construct new resampling algorithms for unbalanced
ranked set samples. We explore the properties of the proposed algorithms. For a
hypothesis testing problem about the underlying population mean, we show that
the bootstrap tests based on the ET estimators of the DF are asymptotically
normal and exhibit a small bias of order $O(n^{-1})$. We illustrate the methods
and evaluate the finite sample performance of the algorithms under both perfect
and imperfect ranking schemes using a real data set and several Monte Carlo
simulation studies. We compare the performance of the test statistics based on
the ET estimators with those based on the empirical likelihood estimators.
