Non-Universal Correction to $Z \to b {\overline b}$ and Single Top Quark Production at Tevatron

New physics associated with the heavy top quark can affect top quark production and the partial decay width of $Z \rightarrow b \bar b$. In this paper, we examine the correlated effects of possible new physics on ${R_b}$ measured at LEP I and the single top quark production rate at Tevatron by using an effective lagrangian technique. We point out that certain operators in the effective lagrangian, constrained by the measured value of $R_b$, can lead to significant and potentially observable effects in single top production.