  The entropy is one of the most applicable uncertainty measures in many
statistical and en- gineering problems. In statistical literature, the entropy
is used in calculation of the Kullback- Leibler (KL) information which is a
powerful mean for performing goodness of fit tests. Ranked Set Sampling (RSS)
seems to provide improved estimators of many parameters of the popu- lation in
the huge studied problems in the literature. It is developed for situations
where the variable of interest is difficult or expensive to measure, but where
ranking in small sub-samples is easy. In This paper, we introduced two
estimators for the entropy and compare them with each other and the estimator
of the entropy in Simple Random Sampling (SRS) in the sense of bias and Root of
Mean Square Errors (RMSE). It is observed that the RSS scheme would improve
this estimator. The best estimator of the entropy is used along with the
estimator of the mean and two biased and unbiased estimators of variance based
on RSS scheme, to esti- mate the KL information and perform goodness of fit
tests for exponentiality and normality. The desired critical values and powers
are calculated. It is also observed that RSS estimators would increase powers.
