Statistical connections between the properties of Type Ia supernovae (SNe Ia) and the B--V colors of their parent galaxies are established. Compared to SNe Ia in blue galaxies [mvtola0.75], SNe Ia in redder galaxies have (1) a wider dispersion in the blueshifts of their Si II lambda6355 absorption features, ten days after maximum light; (2) more rapidly declining light curves; and (3) lower luminosities. Even when the spectroscopically peculiar, very subluminous SNe Ia such as SN 1991bg are disregarded, SNe Ia in red galaxies are less luminous than those in blue galaxies by about 0.3 magnitudes. When SNe Ia that are thought to have been significantly extinguished by dust in their parent galaxies are disregarded, those in blue galaxies have observational absolute--magnitude dispersions of only sigma_{obs}(M_B)=0.20 and sigma_{obs}(M_V)=0.17, which implies that their intrinsic absolute--magnitude dispersions are very small. We use six SNe Ia whose absolute magnitudes have been calibrated by means of Cepheids, which also indicate that the intrinsic absolute--magnitude dispersions of SNe Ia in blue galaxies are very small, to calibrate SNe Ia in blue galaxies and obtain
m H_0=58pm7 km s^{-1} Mpc^{-1}. Implications of the statistical connections between SNe Ia and the colors of their parent galaxies, for identifying the progenitor binary systems of SNe Ia and for using high--redshift SNe Ia to measure q_0, are briefly discussed