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In this paper we report successful synthesis and magnetic properties of (Ca,Na)(Zn,Mn)2Sb2 as a new ferromagnetic dilute magnetic semiconductor (DMS). In this DMS material the concentration of magnetic moments can be controlled independently from the concentration of electric charge carriers that are required for mediating magnetic interactions between these moments. This feature allows us to separately investigate the effect of carriers and of spins on the ferromagnetic properties of this new DMS alloy, and particularly of the critical ferromagnetic behavior. We use modified Arrott plot technique to establish critical exponents b, g, and d of this alloy. We find that at low Mn concentrations (< 10 at.%), it is governed by short-range 3D-Ising behavior, with experimental values of b, g, and d very close to theoretical 3D-Ising values of 0.325, 1.24, and 4.815. However, as the Mn concentration increases, this DMS material exhibits a mixed-phase behavior, with g retaining its 3D-Ising characteristics, but b crossing over to longer-range mean-field behavior.