  The azimuthal asymmetry observed by the HERMES collaboration in
semi-inclusive pion production in deep inelastic scattering of unpolarized
positron on the longitudinally polarized proton target, can provide information
of the quark transversity distributions of the nucleon. We show that the quark
transversity distributions predicted both by the light-cone
quark-spectator-diquark model and by a pQCD inspired model can give consistent
descriptions of the available HERMES data for the analyzing powers
$A_{UL}^{\sin \phi}$ and $A_{UL}^{\sin 2 \phi}$ for $\pi^+$ and $\pi^-$
productions. We also show that the two models give similar predictions of
$A_{UL}^{\sin \phi}$ for $\pi^+$ production, whereas they give very different
predictions of $A_{UL}^{\sin \phi}$ for $\pi^-$ production at large $x$.
Further precision measurement of $A_{UL}^{\sin \phi}$ for $\pi^-$ production
can provide a decisive test of different models.
