  Using a large sample of 90 Seyfert 2 galaxies (Sy2s) with spectropolarimetric
observations, we tested the suggestion that the presence of hidden broad-line
regions (HBLRs) in Sy2s is dependent upon the Eddington ratio. The stellar
velocity dispersion and the extinction-corrected $\OIII$ luminosity are used to
derive the mass of central super-massive black holes and the Eddington ratio.
We found that: (1) below the Eddington ratio threshold of $10^{-1.37}$, all but
one object belong to non-HBLRs Sy2s; while at higher Eddington ratio, there is
no obvious discrimination in the Eddington ratio and black hole mass
distributions for Sy2s with and without HBLRs; (2) nearly all low-luminosity
Sy2s (e.g., $\LOIII < 10^{41} \ergs$) do not show HBLRs regardless of the
column density of neutral hydrogen ($N_{\rm H}$); (3) for high-luminosity Sy2s,
the possibility to detect HBLRs Sy2s is almost the same as that of non-HBLRs
Sy2s; (4) when considering only Compton-thin Sy2s with higher $\OIII$
luminosity ($>10^{41} \ergs$), we find a very high detectability of HBLRs
,$\sim$ 85%. These results suggested that AGN luminosity plays a major role in
not detecting HBLRs in low-luminosity Sy2s, while for high-luminosity Sy2s, the
detectability of HBLRs depends not only upon the AGN activity, but also upon
the torus obscuration.
