We present a joint paper with Anna Seigal, Portia Mira and Miriam Barlow, aimed at addressing the question in the title. Nosocomial outbreaks of bacteria and the heavy usage of antibiotics suggest that resistance evolves in hospital environments. To test this assumption, we studied resistance phenotypes of bacteria collected from patient isolates at a community hospital. A graphical model analysis shows no association between resistance and patient information other than time of arrival. This allows us to focus on time course data. Our main contribution is a statistical hypothesis test called the Nosocomial Evolution of Resistance Detector (NERD). It calculates the significance of resistance trends occurring in a hospital. It can help detect clonal outbreaks, and is available as an R-package. This lecture offers a glimpse into the use of mathematics and statistics in a bio-medical project.