  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 $\pm$ 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 10$\sigma$
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.
