Final answer:
Fran's study will utilize an observational design to compare staff resignation frequencies between two hospital locations without manipulating any variables.
Step-by-step explanation:
The study that Fran is conducting to characterize the frequency of staff resignations between the north and south affiliated hospitals within a hospital system will most likely utilize an observational design. This type of research design is appropriate when the researcher is examining the frequency or patterns of events (such as staff resignations) without manipulating any variables. It allows the researcher to observe the situation as it naturally occurs and then analyze the data to identify any potential differences or trends between the two hospital locations.