The CDF collaboration has set lower limits on the masses of the Z bosons occurring in a range of E_6 GUT based models. We revisit their analysis and extend it to certain other E_6 scenarios as well as to some general classes of models satisfying the
anomaly cancellation conditions, which are not included in the CDF analysis. We also suggest a Bayesian statistical method for finding exclusion limits on the Z mass, which allows one to explore a wide range of the U(1) gauge coupling parameter. This method also takes into account the effects of interference between the Z and the SM gauge bosons.
