  We present a large forward-modeling analysis for 55 late-T (T7-T9) dwarfs,
using low-resolution ($R\approx150$) near-infrared spectra and cloudless
Sonora-Bobcat model atmospheres. We derive the objects' effective temperatures,
surface gravities, metallicities, radii, masses, and luminosities using our
newly developed Bayesian framework, and use the resulting population properties
to test the model atmospheres. We find (1) our objects' fitted metallicities
are 0.3-0.4 dex lower than those of nearby stars; (2) their ages derived from
spectroscopic parameters are implausibly young; (3) their fitted temperatures
show a similar spread as empirical temperature scales at a given spectral type
but are $\sim100$ K hotter for $\geqslant$T8 dwarfs; and (4) their
spectroscopically inferred masses are unphysically small. These results suggest
the Sonora-Bobcat assumptions of cloudless and chemical-equilibrium atmospheres
do not adequately reproduce late-T dwarf spectra. We also find a gravity- and a
metallicity-dependence of temperatures. Combining the resulting parameter
posteriors of our sample, we quantify the degeneracy between surface gravity
and metallicity such that an increase in $Z$ combined with a $3.4\times$
increase in $\log{g}$ results in a spectrum that has similar fitted parameters.
We note the systematic difference between our 1.0-2.5 $\mu$m spectra and the
Sonora-Bobcat models is $\approx$2-4% of the objects' peak $J$-band fluxes,
implying modeling systematics will exceed measurement uncertainties when
analyzing data with $J$-band S/N $\gtrsim50$. Using our large sample, we
examine the fitting residuals as a function of wavelength and atmospheric
properties to discern how to improve the models. Our work constitutes the
largest analysis of brown dwarf spectra using multi-metallicity models and the
most systematic examination of ultracool model atmospheres to date.
