  We present an analysis of three years of precision radial velocity
measurements of 160 metal-poor stars observed with HIRES on the Keck 1
telescope. We report on variability and long-term velocity trends for each star
in our sample. We identify several long-term, low-amplitude radial-velocity
variables worthy of follow-up with direct imaging techniques. We place lower
limits on the detectable companion mass as a function of orbital period. Our
survey would have detected, with a 99.5% confidence level, over 95% of all
companions on low-eccentricity orbits with velocity semi-amplitude K > 100 m/s,
or M_p*sin(i) > 3.0 M_JUP*(P/yr)^(1/3), for orbital periods P< 3 yr. None of
the stars in our sample exhibits radial-velocity variations compatible with the
presence of Jovian planets with periods shorter than the survey duration. The
resulting average frequency of gas giants orbiting metal-poor dwarfs with -2.0
< [Fe/H] < -0.6 is f_p<0.67% (at the 1-sigma confidence level). We examine the
implications of this null result in the context of the observed correlation
between the rate of occurrence of giant planets and the metallicity of their
main-sequence solar-type stellar hosts. By combining our dataset with the
Fischer & Valenti (2005) uniform sample, we confirm that the likelihood of a
star to harbor a planet more massive than Jupiter within 2 AU is a steeply
rising function of the host's metallicity. However, the data for stars with
-1.0 < [Fe/H] < 0.0 are compatible, in a statistical sense, with a constant
occurrence rate f_p~1%. Our results can usefully inform theoretical studies of
the process of giant planet formation across two orders of magnitude in
metallicity.
