  (Abridged) We analyzed the {\it Chandra} and {\it XMM-Newton} archival
observations for 72 type 2 quasars at $z<1$. These objects were was selected
based on the [O III]$\lambda$5007 optical emission line which we assume to be
an approximate indicator of the intrinsic AGN luminosity. We find that the
means of the column density and photon index of our sample are $\log N_{\rm
H}=23.0$ cm$^{-2}$ and $\Gamma=1.87$ respectively, which are consistent with
results from deep X-ray surveys. The observed ratios of hard X-ray and [O III]
line luminosities imply that the majority of our sample suffer significant
amounts of obscuration in the hard X-ray band. A more physically realistic
model which accounts for both Compton scattering and a potential partial
covering of the central X-ray source was used to estimate the true absorbing
column density. We find that the absorbing column density estimates based on
simple power-law models significantly underestimate the actual absorption in
approximately half of the sources. Eleven sources show a prominent Fe K$\alpha$
emission line, and we detect this line in the other sources through a joint fit
(spectral stacking). The correlation between the Fe K$\alpha$ and [O III]
fluxes and the inverse correlation of the equivalent width of Fe K$\alpha$ line
with the ratio of hard X-ray and [O III] fluxes is consistent with previous
results for lower luminosity Seyfert 2 galaxies. We conclude that obscuration
is the cause of the weak hard X-ray emission rather than intrinsically low
X-ray luminosities. We find that about half of the population of
optically-selected type 2 quasars are likely to be Compton-thick. We also find
no evidence that the amount of X-ray obscuration depends on the AGN luminosity
(over a range of more than three orders-of-magnitude in luminosity).
