Epitaxial Zn0.98Mn0.02O thin films were grown on c-cut sapphire substrates under various ambient oxygen pressures (pO2) using pulsed laser deposition. The variation of pO2 during the growth process allowed for the control of intrinsic oxygen vacancies and resulting carrier densities in the films. While no impurity phase contributions were detected, a strong correlation between the effective carrier densities and the observed ferromagnetism (FM) was established. The magnetic data was consistent with a Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange mechanism. The average spin-spin interaction energy for RKKY at 10 K was found to be smaller than the thermal energy, ensuring the availability of carriers to mediate RKKY-type FM, even at low temperatures.