  We present 350 micron polarization observations of four low-mass cores
containing Class 0 protostars: L483, L1157, L1448-IRS2, and Serp-FIR1. This is
the second paper in a larger survey aimed at testing magnetically regulated
models for core-collapse. One key prediction of these models is that the mean
magnetic field in a core should be aligned with the symmetry axis (minor axis)
of the flattened YSO inner envelope (aka pseudodisk). Furthermore, the field
should exhibit a pinched or hour-glass shaped morphology as gravity drags the
field inward towards the central protostar. We combine our results for the four
cores with results for three similar cores that were published in the first
paper from our survey. An analysis of the 350 micron polarization data for the
seven cores yields evidence of a positive correlation between mean field
direction and pseudodisk symmetry axis. Our rough estimate for the probability
of obtaining by pure chance a correlation as strong as the one we found is
about 5%. In addition, we combine together data for multiple cores to create a
source-averaged magnetic field map having improved signal-to-noise ratio, and
this map shows good agreement between mean field direction and pseudodisk axis
(they are within 15 degrees). We also see hints of a magnetic pinch in the
source-averaged map. We conclude that core-scale magnetic fields appear to be
strong enough to guide gas infall, as predicted by the magnetically regulated
models. Finally, we find evidence of a positive correlation between core
magnetic field direction and bipolar outflow axis.
