We estimate the stellar parameters of late K- and early M-type Kepler target stars. We obtain medium-resolution visible spectra of 382 stars with KP - J > 2 (≃K5 and later spectral type). We determine luminosity class by comparing the strength of gravity-sensitive indices (CaH, K I, Ca II, and Na I) to their strength in a sample of stars of known luminosity class. We find that giants constitute 96% ± 1% of the bright (K P < 14) Kepler target stars, and 7% ± 3% of dim (K P > 14) stars, significantly higher than fractions based on the stellar parameters quoted in the Kepler Input Catalog (KIC). The KIC effective temperatures are systematically (110+15 - 35K) higher than temperatures we determine from fitting our spectra to PHOENIX stellar models. Through Monte Carlo simulations of the Kepler exoplanet candidate population, we find a planet occurrence of 0.36 ± 0.08 when giant stars are properly removed, somewhat higher than when a KIC log g > 4 criterion is used (0.27 ± 0.05). Last, we show that there is no significant difference in g - r color (a probe of metallicity) between late-type Kepler stars with transiting Earth-to-Neptune-size exoplanet candidates and dwarf stars with no detected transits. We show that a previous claimed offset between these two populations is most likely an artifact of including a large number of misidentified giants
