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It is well-known that the appearance of measurement errors spoils the traditional results in survey sampling. The concept of correlated measurement errors (CMEs) is true in various practical situations, but this has been seldom considered by researchers in survey sampling. In this article, the influence of the CME under simple random sampling (SRS) has been considered over some prominent classes of estimators for the population mean. The first-order approximated formulae of the mean square error of the introduced estimators are reported, and a comparative analysis has also been conducted with traditional estimators. The theoretical findings are extended by a broad spectrum computational study using real and artificial data.