We study the question of whether the metal-insulator transition in a doped semiconductor takes place in a conduction band or in an impurity band. Our calculations of the Knight shift and the specific heat indicate that the transition takes place in an impurity band. We use a tight-binding model to calculate the electron wavefunctions and density of states and obtain good agreement with the measured Knight shift and specific heat of Si: P. By contrast, the nearly-free-electron model, appropriate to a conduction band, fails to account for the Knight shift measured at the phosphorus nuclei in Si: P.