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We test the predictions of hadronic interaction models regarding the depth ofmaximum of air-shower profiles, $X_{max}$, and ground-particle signals inwater-Cherenkov detectors at 1000 m from the shower core, $S(1000)$, using thedata from the fluorescence and surface detectors of the Pierre AugerObservatory. The test consists in fitting the measured two-dimensional($S(1000)$, $X_{max}$) distributions using templates for simulated air showersproduced with hadronic interaction models EPOS-LHC, QGSJet II-04, Sibyll 2.3dand leaving the scales of predicted $X_{max}$ and the signals from hadroniccomponent at ground as free fit parameters. The method relies on the assumptionthat the mass composition remains the same at all zenith angles, while thelongitudinal shower development and attenuation of ground signal depend on themass composition in a correlated way.  The analysis was applied to 2239 events detected by both the fluorescence andsurface detectors of the Pierre Auger Observatory with energies between$10^{18.5}$ to $10^{19.0}$ eV and zenith angles below $60^\circ$. We found,that within the assumptions of the method, the best description of the data isachieved if the predictions of the hadronic interaction models are shifted todeeper $X_{max}$ values and larger hadronic signals at all zenith angles. Giventhe magnitude of the shifts and the data sample size, the statisticalsignificance of the improvement of data description using the modificationsconsidered in the paper is larger than $5\sigma$ even for any linearcombination of experimental systematic uncertainties.

Testing Hadronic-Model Predictions of Depth of Maximum of Air-Shower  Profiles and Ground-Particle Signals using Hybrid Data of the Pierre Auger  Observatory