SUMMARY
The statistical inference in binomial population is subject to gross errors of estimate, as the samples are not identically distributed. Due to this problem, this work aims to determine which is the best affinity constant (c1) that provides the best performance in the estimator, belonging to the class of E-estimators. With that purpose, the methodology used in this work was applied considering the Monte Carlo simulation method, in which different configurations described by combination of parametric values, levels of contamination and sample sizes were appraised. It was concluded that for the high probability of contamination (? = 0.40), c1 = 0.1 is recommended in cases with large samples (n = 50 and n = 80).