We present experimental results of the first high-precision test of quark-hadron duality in the spin-structure function g_1 of the neutron and $^3$He using a polarized 3He target in the four-momentum-transfer-squared range from 0.7 to 4.0 (GeV/c)^2. Global duality is observed for the spin-structure function g_1 down to at least Q^2 = 1.8 (GeV/c)^2 in both targets. We have also formed the photon-nucleon asymmetry A_1 in the resonance region for 3He and found no strong Q^2-dependence above 2.2 (GeV/c)^2.
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