The Large Binocular Telescope Interferometer (LBTI) is a stellar interferometer consisting of two 8.4-m apertures on a 14.4 m baseline on a common mount at Mt. Graham, Arizona. The Hunt for Observable Signatures of Terrestrial Systems (HOSTS) is a NASA key project for the LBTI surveying the warm and hot dust in the inner regions of planetary systems, near the habitable zone (HZ) and closer in, commonly described as being 'exo-zodiacal,' analogous to the zodiacal light in our Solar System. The presence of large amounts of dust in the HZs of nearby stars poses a significant challenge for target selection and planning of future exo-Earth imaging missions. The HOSTS survey on the LBTI is designed to determine typical exozodi levels around a sample of nearby, bright main sequence stars. The LBTI operates in a nulling mode in the mid-infrared spectral window (8-13ϵ m), in which light from the two telescopes is coherently combined with a 180-degree phase shift between them, producing a dark fringe at the location of the target star. In doing so the starlight is greatly reduced, increasing the contrast, analogous to a coronagraph operating at shorter wavelengths. The LBTI is a unique instrument, having only three warm reflections before the starlight reaches cold mirrors, giving it the best photometric sensitivity of any interferometer operating in the mid-infrared. It also has a superb Adaptive Optics (AO) system giving it Strehl ratios greater than 98% at 10ϵ m. Thus, nulling interferometry suppresses the bright stellar light and allows for the detection of faint, extended circumstellar dust emission. In this paper we present statistical results from 38 individual stars. We provide important new insights into the incidence rate, typical levels, and origin of HZ dust around main sequence stars. Our overall detection rate is 23%. While the inferred occurrence rates are comparable for early type and Sun-like stars, but decrease from [71 (+11/-20)] % for stars with previously detected mid to far infrared excess to [11 (+9/-4)]% for stars without such excess, confirming earlier results at high confidence. For completed observations on individual stars, our sensitivity is five to ten times better than previous results. Assuming a lognormal excess luminosity function, we put upper limits on the median HZ dust level of 11.5 zodis (95% confidence) for all stars without cold dust and of 16 zodis when focussing on Sun-like stars without cold dust. We find first hints of a bimodal distribution where some stars have high HZ dust levels but the majority have dust levels below our sensitivity. Our results demonstrate the strength of LBTI for vetting potential targets for future exo-Earth imaging missions.