We test the homogeneity of the universe at z~0.3 with the luminous redgalaxy (LRG) spectroscopic sample of the Sloan Digital Sky Survey.First, the mean number N(R) of LRGs within completely surveyedLRG-centered spheres of comoving radius R is shown to be proportional toR^{3} at radii greater than R~70h^{-1}Mpc. The test hasthe virtue that it does not rely on the assumption that the LRG samplehas a finite mean density; its results show, however, that there is sucha mean density. Second, the survey sky area is divided into 10 disjointsolid angular regions, and the fractional rms density variations of theLRG sample in the redshift range 0.27h^{-3}Mpc^{3}) regions is found