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.
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