Angular distributions of the analyzing power ${A}_{y}(\ensuremath{\theta})$ for the elastic n-$^{4}\mathrm{He}$ scattering have been measured in the energy range 15-50 MeV. A continuous energy polarized neutron beam was produced using a 52 MeV polarized deuteron beam incident on a liquid deuterium target. A liquid helium scintillation detector was used as a scattering sample. Scattered neutrons were detected with 14 scintillation detectors. Multiparameter data acquisition was performed to discriminate against background events. The incident neutron energy was determined off line by cuts in the incident time-of-flight spectra. The data were normalized in the backward angle maxima by previous N-$^{4}\mathrm{He}$ data. The results were used as input in a series of phase shift analyses. Coulomb correction procedures to p-$^{4}\mathrm{He}$ phase shifts have been used to provide n-$^{4}\mathrm{He}$ predictions. The validity of these procedures has been tested. A set of n-$^{4}\mathrm{He}$ phase shifts, varying smoothly with energy, is given which reproduces the new data very well.