  We extend our previous work on the precision electroweak tests in the Sp(6)_L
X U(1)_Y family model to include for the first time the important Z->b b-bar
vertex corrections encoded in a new variable epsilon_b, utilizing all the
latest LEP data. We include in our analysis the one loop EW radiative
corrections due to the new bosons in terms of epsilon_1, epsilon_b and
$\Delta\Gamma_Z$. We find that the correlation between epsilon_1 and epsilon_b
makes the combined constraint much stronger than the individual ones. The model
is consistent with the recent CDF result of $m_t=174\pm 10^{+13}_{-12}\GeV$,
but it can not accomodate $m_t\gsim 195\GeV$.
