  We study the single spin asymmetry in the transversely polarized proton
production and the lambda hyperon production in semi-inclusive deep inelastic
scattering with a $\sin \phi_{S_h}$ modulation, in which $S_h$ is the azimuthal
angle of the transverse spin of the final hadron. The theoretical
interpretation for the asymmetry is presented as the convolution of the twist-3
quark transverse momentum dependent distributions and twist-2 fragmentation
functions. We investigate the role of the twist-3 distribution functions $h(x,
p_T^2)$, $f^\perp(x, p_T^2)$ and $g^\perp(x, p_T^2)$ and the twist-2
fragmentation functions $H_1(x, k_T^2)$, $D_{1T}^\perp(x, k_T^2)$ and
$G_{1T}(x, k_T^2)$ in this asymmetry. Using spectator model, we compute these
distribution and fragmentation functions and estimate the $\sin \phi_{S_h}$
asymmetry for the proton production as well as for the lambda production at
JLab with a 12 $\mathrm{GeV}$ electron beam. The asymmetry at the COMPASS
kinematics is also predicted. By comparing different sources for the asymmetry,
we conclude that it is feasible to access the distribution function $h$ and the
fragmentation function $H_1$ through measuring the asymmetry in the proton
production, whereas the $f^\perp \,D_{1T}^\perp$ term might be probed in the
lambda production at JLab 12 GeV.
