We present the results of a search for new particles that lead to a Z boson plus jets in pp collisions at 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 μμ 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 tt 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/c2 are excluded at 95% confidence level.