We report manipulation of the atom number statistics associated with Bose-Einstein condensed atoms confined in an array of weakly Linked mesoscopic traps. We used the interference of atoms released from the traps as a sensitive probe of these statistics. By controlling relative strengths of the tunneling rate between traps and atom-atom interactions within each trap, we observed trap states characterized by sub-Poissonian number fluctuations and adiabatic transitions between these number-squeeled states and coherent states of the atom field. The quantum states produced in this work may enable substantial gains in sensitivity for atom interference-based instruments as well as fundamental studies of quantum phase transitions.