  We use the physically-consistent tilted spatially-flat and untilted non-flat
$\Lambda$CDM inflation models to constrain cosmological parameter values with
the Planck 2015 cosmic microwave background (CMB) anisotropy data and recent
Type Ia supernovae measurements, baryonic acoustic oscillations (BAO) data,
growth rate observations, and Hubble parameter measurements. The most dramatic
consequence of including the four non-CMB data sets is the significant
strengthening of the evidence for non-flatness in the non-flat $\Lambda$CDM
model, from 1.8$\sigma$ for the CMB data alone to 5.1$\sigma$ for the full data
combination. The BAO data is the most powerful of the non-CMB data sets in more
tightly constraining model parameter values and in favoring a spatially-closed
Universe in which spatial curvature contributes about a percent to the current
cosmological energy budget. The untilted non-flat $\Lambda$CDM model better
fits the large-angle CMB temperature anisotropy angular spectrum and is more
consistent with the Dark Energy Survey constraints on the current value of the
rms amplitude of mass fluctuations ($\sigma_8$) as a function of the current
value of the nonrelativistic matter density parameter ($\Omega_m$) but does not
provide as good a fit to the smaller-angle CMB temperature anisotropy data as
does the tilted flat-$\Lambda$CDM model. Some measured cosmological parameter
values differ significantly between the two models, including the reionization
optical depth and the baryonic matter density parameter, both of whose
2$\sigma$ ranges (in the two models) are disjoint or almost so.
