We present the results of a search for new particles that lead to a Z boson plus jets in p (p) over bar collisions at root s=1.96 TeV using the Collider Detector at Fermilab (CDF II). A data sample with a luminosity of 1.06 fb(-1) collected using Z boson decays to ee and mu mu is used. We describe a completely data-based method to predict the dominant background from standard model Z + jet events. This method can be similarly applied to other analyses requiring background predictions in multijet environments, as shown when validating the method by predicting the background from W + jets in t (t) over bar production. No significant excess above the background prediction is observed, and a limit is set using a fourth generation quark model to quantify the acceptance. Assuming BR(b(')-> bZ)=100% and using a leading-order calculation of the b(') cross section, b(') quark masses below 268 GeV/c(2) are excluded at 95% confidence level.