Magnetic properties of Ising nanoparticles with spin-1/2 core and spin-3/2 shell structure are systematically studied by the use of the effective-field theory with correlations. Particular emphasis is given to the effects of the crystal-field, core and shell interactions and interface coupling on magnetizations, compensations points, magnetic susceptibilities and hysteresis behaviors. In order to confirm the stability of the solutions we also investigate the free energy of the system. According to values of Hamiltonian parameters, the system only undergoes a second-order phase transition. A number of characteristic behaviors are found, such as the existence of triple hysteresis loops for appropriate values of the system parameters affected by the crystal field, temperature, and interface coupling. Moreover, Q-, R-, N-, M-, P- and S-types of compensation behaviors in the Neel classification nomenclature exist in the system that are also strongly dependent on interaction parameters; hence, one or two compensation points have been found. The results are compared with those of recently published works and a qualitatively good agreement is found.