  We use polarized inelastic neutron scattering (INS) to study spin excitations
of optimally hole-doped superconductor Ba$_{0.67}$K$_{0.33}$Fe$_2$As$_{2}$
($T_c=38$ K).
  In the normal state, the imaginary part of the dynamic susceptibility,
$\chi^{\prime\prime}(Q,\omega)$, shows magnetic anisotropy for energies below
$\sim$7 meV with c-axis polarized spin excitations larger than that of the
in-plane component. Upon entering into the superconducting state, previous
unpolarized INS experiments have shown that spin gaps at $\sim$5 and 0.75 meV
open at wave vectors $Q=(0.5,0.5,0)$ and $(0.5,0.5,1)$, respectively, with a
broad neutron spin resonance at $E_r=15$ meV. Our neutron polarization analysis
reveals that the large difference in spin gaps is purely due to different spin
gaps in the c-axis and in-plane polarized spin excitations, resulting resonance
with different energy widths for the c-axis and in-plane spin excitations. The
observation of spin anisotropy in both opitmally electron and hole-doped
BaFe$_2$As$_2$ is due to their proximity to the AF ordered BaFe$_2$As$_2$ where
spin anisotropy exists below $T_N$.
