  We study the shot noise (nonequilibrium current fluctuation) associated with
dynamic nuclear polarization in a nonequilibrium quantum wire (QW) fabricated
in a two-dimensional electron gas. We observe that the spin-polarized
conductance quantization of the QW in the integer quantum Hall regime collapses
when the QW is voltage biased to be driven to nonequilibrium. By measuring the
shot noise, we prove that the spin polarization of electrons in the QW is
reduced to $\sim 0.7$ instead of unity as a result of electron-nuclear
spin-flip scattering. The result is supported by Knight shift measurements of
the QW using resistively detected NMR.
