We report on measurements of the neutron spin asymmetries $A_{1,2}^n$ and polarized structure functions $g_{1,2}^n$ at three kinematics in the deep inelastic region, with $x=0.33$, 0.47 and 0.60 and $Q^2=2.7$, 3.5 and 4.8 (GeV/c)$^2$, respectively. These measurements were performed using a 5.7 GeV longitudinally-polarized electron beam and a polarized $^3$He target. The results for $A_1^n$ and $g_1^n$ at $x=0.33$ are consistent with previous world data and, at the two higher $x$ points, have improved the precision of the world data by about an order of magnitude. The new $A_1^n$ data show a zero crossing around $x=0.47$ and the value at $x=0.60$ is significantly positive. These results agree with a next-to-leading order QCD analysis of previous world data. The trend of data at high $x$ agrees with constituent quark model predictions but disagrees with that from leading-order perturbative QCD (pQCD) assuming hadron helicity conservation. Results for $A_2^n$ and $g_2^n$ have a precision comparable to the best world data in this kinematic region. Combined with previous world data, the moment $d_2^n$ was evaluated and the new result has improved the precision of this quantity by about a factor of two. When combined with the world proton data, polarized quark distribution functions were extracted from the new $g_1^n/F_1^n$ values based on the quark parton model. While results for $Delta u/u$ agree well with predictions from various models, results for $Delta d/d$ disagree with the leading-order pQCD prediction when hadron helicity conservation is imposed.
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