  We forecast the sensitivity with which the Murchison Widefield Array (MWA)
can measure the 21 cm power spectrum of cosmic hydrogen, using radiative
transfer simulations to model reionization and the 21 cm signal. The MWA is
sensitive to roughly a decade in scale (wavenumbers of k ~ 0.1 - 1 h Mpc^{-1}),
with foreground contamination precluding measurements on larger scales, and
thermal detector noise limiting the small scale sensitivity. This amounts
primarily to constraints on two numbers: the amplitude and slope of the 21 cm
power spectrum on the scales probed. We find, however, that the redshift
evolution in these quantities can yield important information about
reionization. Although the power spectrum differs substantially across
plausible models, a generic prediction is that the amplitude of the 21 cm power
spectrum on MWA scales peaks near the epoch when the intergalactic medium (IGM)
is ~ 50% ionized. Moreover, the slope of the 21 cm power spectrum on MWA scales
flattens as the ionization fraction increases and the sizes of the HII regions
grow. Considering detection sensitivity, we show that the optimal MWA antenna
configuration for power spectrum measurements would pack all 500 antenna tiles
as close as possible in a compact core. The MWA is sensitive enough in its
optimal configuration to measure redshift evolution in the slope and amplitude
of the 21 cm power spectrum. Detecting the characteristic redshift evolution of
our models will confirm that observed 21 cm fluctuations originate from the
IGM, and not from foregrounds, and provide an indirect constraint on the
volume-filling factor of HII regions during reionization. After two years of
observations under favorable conditions, the MWA can constrain the filling
factor at an epoch when <x_i> ~ 0.5 to within roughly +/- 0.1 at 2-sigma.
