The free surface of water, and the interface between water and a hydrophobic surface, both have positive interface energies. The water density near a free surface drops below the bulk density, and thus it is expected that water near a hydrophobic surface will also show a density depletion.However, efforts by multiple groups to detect and characterize the predicted 'gap' at waterhydrophobic interfaces have produced contradictory results. We have studied the interface between water and fluoroalkylsilane self-assembled monolayers using specular X-ray reflectivity, and analyzed the parameter-space landscapes of the merit functions being minimized by data fitting. This analysis yields a better understanding of confidence intervals than the customary process of reporting a unique 'best' fit. We conclude that there are unambiguous gaps at water-hydrophobic interfaces when the hydrophobic monolayer is more densely packed.