Aresearcher wishes to conduct a study on the relationship between paternal care giving (that is, the care the prisoner subjects received as children from their fathers) and incarceration, using a short 15-minute survey. which category applies to this research?

I believe the answer is: category i
Category i is the type of study that is conducted in order to found a possible cause and effect of a certain situation.
This type of study is commonly presents no more than a minimal risk and the subjects wouldn't feel any inconvenient because of their participation.