Studies of the NMR Knight shift K of Na 0:3 CoO 2 . yH 2 O have been carried out in detail. The suppression of K by the occurrence of the superconductivity reported previously by the present authors in both magnetic field directions perpendicular and parallel to the c-axis has been confirmed, indicating that the Cooper pairs are in the singlet state. The anisotropy of the suppression amplitudes is consistent with the anisotropy of the hyperfine coupling constant A spin estimated from the K-plot. It has also been found that even samples that do not exhibit a significant the Curie-Weiss-like increase of the uniform magnetic susceptibility with decreasing temperature T, exhibit superconducting transition, which indicates that the superconducting Na 0:3 CoO 2 . 1.3H 2 O is not necessarily in the region of proximity of the ferromagnetic phase. It has also been confirmed that the superconducting transition temperature T c of the samples prepared by mixing Na 0:7 CoO 2 , H 2 O (or D 2 O) and bromine for 4 h, and separating the resultant powder from the solution by filtration, depends on the elapsed time t after filtration. For these samples, the Curie-Weiss component of estimated at low temperatures increases with t, supporting the idea that the number of lattice imperfections possibly due to oxygen-vacancy formation increases with t. Even for such samples, the superconductivity appears, which seems to exclude the possibility of an anisotropic superconducting order parameter. These results are favorable for full-gapped superconductivity.