Monte Carlo simulations are used for many problems in proton radiation therapy, some of which are sensitive to the nuclear interaction model. The available models have been little tested in the regime of interest, namely in their ability to predict the secondary particle yield, including their angle and energy, when 70-250 MeV protons stop in various materials. The present study provides one such test in carbon, complementing a previous one in copper. Using a multilayer Faraday cup we have measured the projected range distribution of charged nuclear secondaries from 160 MeV protons stopping in polyethylene (CH2). To test the popular GEANT Monte Carlo we have simulated the experiment with GEANT3 using the "Gheisha" (default) and "Fluka" models and with GEANT4.5 using the "low-energy" and "precompound" models. The GEANT3/Fluka and GEANT4/precompound simulations agree moderately well with the observed range distribution. The data are given in a convenient form for testing other Monte Carlo programs.