  We present experimental evidence that the effective medium approximation
(EMA), developed by D.C. Morse [Phys. Rev. E {\bf 63}, 031502, (2001)],
provides the correct scaling law of the macroscopic plateau modulus
$G^{0}\propto\rho^{4/3}L^{-1/3}_{p}$ (where $\rho$ is the contour length per
unit volume and $L_{p}$ is the persistence length) of semi-flexible polymer
solutions, in the highly entangled concentration regime. Competing theories,
including a self-consistent binary collision approximation (BCA), have instead
predicted $G^{0}\propto\rho^{7/5}L^{-1/5}_{p}$. We have tested both the EMA and
BCA scaling predictions using actin filament (F-actin) solutions which permit
experimental control of $L_p$ independently of other parameters. A combination
of passive video particle tracking microrheology and dynamic light scattering
yields independent measurements of the elastic modulus $G$ and $L_{p}$
respectively. Thus we can distinguish between the two proposed laws, in
contrast to previous experimental studies, which focus on the (less
discriminating) concentration functionality of $G$.
