  We present a search for standard model Higgs boson production in association
with a W boson in proton-antiproton collisions ($p\bar{p}\to W^\pm H \to
\ell\nu b\bar{b}$) at a center of mass energy of 1.96 TeV. The search employs
data collected with the CDF II detector which correspond to an integrated
luminosity of approximately 1 fb-1. We select events consistent with a
signature of a single lepton ($e^\pm/\mu^\pm$), missing transverse energy, and
two jets. Jets corresponding to bottom quarks are identified with a secondary
vertex tagging method and a neural network filter technique. The observed
number of events and the dijet mass distributions are consistent with the
standard model background expectations, and we set 95% confidence level upper
limits on the production cross section times branching ratio ranging from 3.9
to 1.3 pb for Higgs boson masses from 110 to 150 GeV/c2, respectively.
