Dark matter appears inevitablefor explaining the observed kinematics of galaxies, galaxy clusters, and thewhole Universe. Gravitational (both weak and strong) lensing observations alsoclearly require dark matter. Such inference of dark matter based on Einstein’s theory of gravity or its non-relativistic limit of Newton’s theory is challenged by the observed existence of a criticalacceleration a0 and a remarkably simple explanation of observed galaxy rotationcurves based on it. This modified Newtonian dynamics (MOND) is furthersupported by the extremely tight Baryonic Tully-Fisher relation preciselymatching a0. While dynamical analyses of a large statistical sample ofelliptical galaxies are interesting in its own right, they may provide aninteresting leverage in testing dark matter and modified Newtonian dynamics. Wecollect large numbers of spherical and disk-less galaxies from theSloan Digital Sky Survey with the 2-dimensional structural parameters, stellarmasses and aperture velocity dispersions measured. We then use the sphericalJeans equation to obtain a statistical sample of models of spherical galaxies.By analyzing the predicted velocity dispersion profiles in the sample weconstrain dark halo parameters and MOND parameters and test the competingparadigms. Some results are presented and discussed.