  We study observational constraints on the assisted k-inflation models in
which multiple scalar fields join an attractor characterized by an effective
single field $\phi$. This effective single-field system is described by the
Lagrangian $P=Xg(Y)$, where $X$ is the kinetic energy of $\phi$, $\lambda$ is a
constant, and $g$ is an arbitrary function in terms of $Y=X e^{\lambda \phi}$.
Our analysis covers a wide variety of k-inflation models such as dilatonic
ghost condensate, Dirac-Born-Infeld (DBI) field, tachyon, as well as the
canonical field with an exponential potential. We place observational bounds on
the parameters of each model from the WMAP 7yr data combined with Baryon
Acoustic Oscillations (BAO) and the Hubble constant measurement. Using the
observational constraints of the equilateral non-Gaussianity parameter
$f_{NL}^{equil}$, we further restrict the allowed parameter space of dilatonic
ghost condensate and DBI models. We extend the analysis to more general models
with several different choices of $g(Y)$ and show that the models such as
$g(Y)=c_0+c_p Y^p$ ($p \ge 3$) are excluded by the joint data analysis of the
scalar/tensor spectra and primordial non-Gaussianities.
