We present full results of a wide-energy, population study of X-ray em
ission from a sample of 51 candidate starburst galaxies selected from
the IRAS Bright Galaxy Sample. Super posed low and high energy X-ray e
mission from these galaxies in the Einstein IPC and HEAO-1 A2 and A4 e
nergy bands, which span 0.5 to 160 keV, is detected at the 99.99% conf
idence level, after allowing for confusion noise in the HEAO-1 data. A
bove 13 keV the confidence level is only 85%. A power-law fit to the m
ean spectral luminosity yields a (photon) index of 1.47 +/- 0.26. We c
onsider and assess likely environments and mechanisms for X-ray emissi
on in starburst galaxies. These include thermal emission from massive
binaries, supernova remnants, and galactic halos, and nonthermal emiss
ion resulting from Compton scattering of relativistic electrons by the
far IR and the cosmic microwave background radiation fields. The cont
ribution of the population of sources represented by this sample to th
e 3-50 keV residual cosmic X-ray background is estimated to be at the
3 - -4% level assuming no evolution. This contribution is significantl
y higher if the population evolved moderately.