We present the results of high-statistics calculations of correlation functions generated with single-baryon interpolating operators on an ensemble of dynamical anisotropic gauge-field configurations generated by the Hadron Spectrum Collaboration using a tadpole-improved clover fermion action and Symanzik-improved gauge action. A total of 292, 500 sets of measurements are made using 1194 gauge configurations of size 20 3 × 128 with an anisotropy parameter ξ = b s / b t = 3.5 , a spatial lattice spacing of b s = 0.1227 ± 0.0008     fm , and pion mass of M π ∼ 390     MeV . Ground state baryon masses are extracted with fully quantified uncertainties that are at or below the ∼ 0.2 % -level in lattice units. The lowest-lying negative-parity states are also extracted albeit with a somewhat lower level of precision. In the case of the nucleon, this negative-parity state is above the N π threshold and, therefore, the isospin- 1 2 π N s -wave scattering phase-shift can be extracted using Lüscher's method. The disconnected contributions to this process are included indirectly in the gauge-field configurations and do not require additional calculations. The signal-to-noise ratio in the various correlation functions is explored and is found to degrade exponentially faster than naive expectations on many time slices. This is due to backward propagating states arising from the antiperiodic boundary conditions imposed on the quark propagators in the time direction. We explore how best to distribute computational resources between configuration generation and propagator measurements in order to optimize the extraction of single baryon observables.