If the auxiliary variable coefficient of variation c_x is known but negligible, then what comes of the mean square error (mse) of our conventional product and mean per unit estimators. In this study, if c_x is known but negligible, that is, if it tend towards zero (c_x→0), the mse of both the conventional product and mean per unit estimator becomes equal. The question that will quickly come to mind here is, how often does known becomes negligible?. It at times do occur in sample survey, so there must be statistical awareness on this in case we experience such in our researches, just like when the population size (N) is large, then, the finite population correction (fpc) becomes negligible and hence, it tends towards zero (f=n/N→0). If c_x→0, then virtually the mse of some of the existing proposed alternatives may tend towards the mse of the mean per unit estimator. When this occur, over estimation problem in product estimation does not arise but if known c_x is not negligible, Adewara (2016) proposed an alternative product estimator, ӯ_aaap, which utilizes c_x which was found to minimize over estimation of ӯ_p on ӯ whenever ρ_xy < [c_y²*(1-α²*(Ẍ/(Ẍ+c_x)²)-α²*(Ẍ/(Ẍ+c_x))²*c_x²]/[2*c_y*c_x*α²*(Ẍ/(Ẍ+c_x))²], 0.1 <= α <0.7.