How do the sampling methods and sample sizes vary for the different types of quantitative and qualitative research?

 For my proposed PICOT question, I have chosen patient safety. (P) In a hospice facility, (I) how does lowering nurse to patient ration to 1:4, (C) compared to having nurse to patient ratio 1:5, (O) help improve pain management and comfort measures, (T) in a 6-month period.  This question is one I wonder how it will impact providing end of life care.