A scheme is proposed to manipulate the quantum-statistical properties of a neutral atomic Bose-Einstein condensate in an ultracold alkali-atom-trap system with atoms in the ground hyperfine F=1, ${\mathit{M}}_{\mathit{F}}$=\ifmmode\pm\else\textpm\fi{}1,0 states (labeled respectively as \ensuremath{\Vert}${\mathit{g}}_{\ifmmode\pm\else\textpm\fi{},0}$〉). Initially, the atomic condensate is assumed to be prepared in a hyperfine sublevel \ensuremath{\Vert}${\mathit{g}}_{\mathrm{\ensuremath{-}}}$〉. By effective two-photon excitations with two classical (${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$) and quantum (${\mathrm{\ensuremath{\sigma}}}^{+}$) nonresonant copropagating traveling-wave light fields, we show that the atomic system can be settled into a coherent superposition of two atomic Bose-Einstein condensates corresponding to different ground hyperfine sublevels and different quantum statistics. Furthermore, with an appropriate choice of interaction time, atom-field coupling strengths, and quantum features of the quantized laser field, a nonclassical condensate can be prepared in the hyperfine sublevel \ensuremath{\Vert}${\mathit{g}}_{+}$〉.