Final answer:
The nurse researcher is using inductive reasoning to arrive at a general conclusion based on observed related observations.
Step-by-step explanation:
The nurse researcher is using inductive reasoning. Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. In this case, the nurse researcher has observed that nausea and vomiting are common side effects of chemotherapy, and based on this observation, they are making the general conclusion that patients with leukemia who are undergoing chemotherapy are likely to experience nausea and vomiting.