We have measured the mechanical properties of coagulation-spun polymer-nanotube composite fibers. Both the fiber modulus, Y, and strength, sigma(B), scale linearly with volume fraction, V-f, up to V-f similar to 10%, after which these properties remain constant. We measured dY/dV(f) = 254 GPa and d sigma(B)/dV(f) = 2.8 GPa in the linear region. By drawing fibers with V-f < 10% to a draw ratio of similar to 60%, we can increase these values to dY/dV(f) = 600 GPa and d sigma(B)/dV(f) = 7 GPa. Raman measurements show the Herman's orientation parameter, S, to increase with drawing, indicating that significant nanotube alignment occurs. Raman spectroscopy also shows that the nanotube effective modulus, Y-Eff, also increases with drawing. We have calculated an empirical relationship between the nanotube orientation efficiency factor, eta(o), and S. This allows us to fit the data for Y-Eff versus eta(o), showing that the fiber modulus scales linearly with eta(o), as predicted theoretically by Krenchel. From the fit, we estimate the nanotube modulus to be; Y-NT = 480 GPa. Finally, we show that the fiber strength also scales linearly with eta(o), giving an effective interfacial stress transfer of tau = 40 MPa and a nanotube critical length of I-c = 1250 nm. This work demonstrates the validity of the Cox-Krenchel rule of mixtures and shows that continuum theory still applies at the near-molecular level.