A facility that can deliver beams of electron and muon neutrinos from the decay of a stored muon beam has the potential to unambiguously resolve the issue of the evidence for light sterile neutrinos that arises in short-baseline neutrino oscillation experiments and from estimates of the effective number of neutrino flavors from fits to cosmological data. In this paper, we show that the nuSTORM facility, with stored muons of 3.8 GeV/c ± 10%, will be able to carry out a conclusive muon neutrino appearance search for sterile neutrinos and test the LSND and MiniBooNE experimental signals with 10σ sensitivity, even assuming conservative estimates for the systematic uncertainties. This experiment would add greatly to our knowledge of the contribution of light sterile neutrinos to the number of effective neutrino flavors from the abundance of primordial helium production and from constraints on neutrino energy density from the cosmic microwave background. The appearance search is complemented by a simultaneous muon neutrino disappearance analysis that will facilitate tests of various sterile neutrino models.