Thermoelectric $Zn_4Sb_3$ alloys were synthesized by a conventional powder metallurgy process consisting of solid state reaction and hot pressing. Single phase $Zn_4Sb_3$ was successfully produced by the annealing of cold compact starting with the mixed elemental powders, and subsequent hot pressing yielded single phase bulk specimens without microcracks. Phase transformations in this alloy system during synthesis were investigated using XRD, SEM and EDS. Thermoelectric properties as a function of temperature were investigated from room temperature to 600 K and compared with results of analogue studies. Transport properties at room temperature were also evaluated. Thermoelectric properties of single phase $Zn_4Sb_3$ materials produced by this process are comparable to the published data. Synthesis by solid state reaction and hot pressing offers a potential processing route to produce a bulk $Zn_4Sb_3$.