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+-% of the bright (Kp<14) Kepler target stars, and 7+-3% of dim (Kp>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 -35} K) 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). Lastly, 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 sized 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.