  The possibility exists that cosmic-ray neutrinos with energies of $\sim
10^{20}$ eV interact in the atmosphere with a cross section at the millibarn
level, giving rise to some of the highest-energy air showers. In a specific
dynamical model which can give rise to such a cross section, we show that there
can be a small effect upon the extraction of the effective value of $\sin^2
\theta_W$ from $\nu_\mu$-hadron, neutral-current cross section data at NuTeV.
