High-Redshift Quasars Found in Sloan Digital Sky Survey Commissioning Data III: A Color Selected Sample at i^*<20 in the Fall Equatorial Stripe

This is the third paper in a series aimed at finding high-redshift quasars from five-color (u'g'r'i'z') imaging data taken along the Celestial Equator by the SDSS during its commissioning phase. In this paper, we first present the observations of 14 bright high-redshift quasars (3.66<z<4.77, i^*<20) discovered in the SDSS Fall Equatorial Stripe, and the SDSS photometry of two previously known high-redshift quasars in the same region of the sky. Combined with the quasars presented in previous papers, we define a color-selected flux-limited sample of 39 quasars at 3.6 < z < 5.0 and i^*<20, covering a total effective area of 182 deg^2. From this sample, we estimate the average spectral power law slope in the rest-frame ultraviolet for quasars at z~4 to be -0.79 with a standard deviation of 0.34, and the average rest-frame equivalent width of the Ly alpha+N V emission line to be 69 A with a standard deviation of 18 A. The selection completeness of this multicolor sample is determined from the model colors of high-redshift quasars, taking into account the distributions of emission line strengths, intrinsic continuum slope, the line and continuum absorption from intervening material, and the effects of photometric errors. The average completeness of this sample is about 75%. The selection function calculated in this paper will be used to correct the incompleteness of this color-selected sample and to derive the high-redshift quasar luminosity function in a subsequent paper. In the Appendix, we present the observations of an additional 18 faint quasars (3.57<z<4.80, 20.1<i^*