At the Fermilab Tevatron proton-antiproton (pp¯) collider, Drell-Yan lepton pairs are produced in the process pp¯→e+e-+X through an intermediate γ*/Z boson. The forward-backward asymmetry in the polar-angle distribution of the e- as a function of the e+e--pair mass is used to obtain sin2θefflept, the effective leptonic determination of the electroweak-mixing parameter sin2θW. The measurement sample, recorded by the Collider Detector at Fermilab (CDF), corresponds to 9.4 fb-1 of integrated luminosity from pp¯ collisions at a center-of-momentum energy of 1.96 TeV, and is the full CDF Run II data set. The value of sin2θefflept is found to be 0.23248±0.00053. The combination with the previous CDF measurement based on μ+μ- pairs yields sin2θefflept=0.23221±0.00046. This result, when interpreted within the specified context of the standard model assuming sin2θW=1-MW2/MZ2 and that the W- and Z-boson masses are on-shell, yields sin2θW=0.22400±0.00045, or equivalently a W-boson mass of 80.328±0.024 GeV/c2.