Next-generation space observatories will conduct the first systematic search for life beyond the Solar System. Through statistical analyses of a large enough sample of exoplanets, such surveys could answer questions about what makes planets habitable and how terrestrial planets evolve. We describe our code, Bioverse, which assesses the potential of future exoplanet observatories to test specific statistical hypotheses as a function of their design, survey strategy, and statistical sources of noise. In two examples of its usage, we explore the requirements for conceptual next-generation observatories to (i) test the habitable zone concept and (ii) study the oxygen evolution of inhabited planets. Our analysis factors in realistic simulations of direct imaging and transit spectra (including the effects of cloud cover) and considers a range of values for yet-unknown astrophysical parameters (such as the frequency of habitable and inhabited worlds). These results — representing two of the many potential cases which Bioverse can address — will help to maximize the scientific output of future flagship missions.