The refractive index dependence of the spontaneous emission rate is determined using organically capped CdSe and CdTe quantum dots as probes. The radiative lifetime of the exciton emission is measured in a variety of apolar solvents with refractive indices n between 1.37 and 1.50. It is demonstrated that quantum dots provide a model system for testing theories on the influence of local-field effects on the spontaneous emission rate. The experimentally observed influence of n on the radiative lifetime is smaller than predicted by well-known models for local-field corrections but is in good agreement with a recently developed fully microscopic model for the local-field enhancement of the spontaneous emission rate.