  We perform a joint analysis of the prediction of composite Higgs models for
the discrepancies of the forward-backward asymmetries of top and bottom quarks
at Tevatron and LEP+SLC, respectively. We build a two sector model which can be
thought as an effective low energy description of 5D warped models and choose
the quantum numbers of the fermionic resonances to protect the Z-couplings of
the partially composite Standard Model light quarks. We analyze the cross
section, forward-backward asymmetry and invariant mass distribution of the top
anti-top production at Tevatron, as well as the bottom forward-backward
asymmetry and the Z-branching fraction into b-quarks at LEP and SLC, for the
two sector model. In the region of the parameter space that naturally leads to
the Standard Model spectrum and solves the bottom anomaly, the model improves
the top forward-backward asymmetry, giving a prediction of up to 10%, and
predicts a small decrease of the $t \bar t$ cross section. It also predicts
non-universal corrections of the Z-couplings to the light quarks of order
0.001.
