We analyze the millimeter intensity spectrum expected from the dynamic model of Carlsson & Stein together with the interferometric observations of the quiet Sun obtained at a wavelength of 3.5 mm with the Berkeley-Illinois- Maryland Array. The observational data products (Fourier and wavelet spectra, brightness histograms) are compared with the corresponding products obtained for the Carlsson & Stein (CS) models. We estimate how the limited spatial resolution of the observations influences the comparison with the predictions of chromospheric dynamic models and discuss the limitations of a one-dimensional non-magnetic modeling approach. In addition, we test the effect of the integration time of the BIMA observations on the dynamic signatures. The dependence of the observed brightness variations on spatial resolution is studied by employing artificial image degradation and approximating the obtained dependence by power laws. We are able to establish a correspondence between the CS model predictions and the obse