Answer: Paul is conducting a "QUANTITATIVE RESEARCH".
Explanation: Quantitative research is a type of research where data is collected in numbers and compared, using statistical method. Quantitative research helps researchers to compare each variable in a result, to get a difference and similarities in a mathematical model.
Paul has conducted a survey to get informations, which includes family size and ethnicity. This family size will be in numbers, and will probably be compared among families of different ethnicity. This makes this research a Quantitative research.