Final answer:
The chicken salad should not be served at the nursing home's barbecue as it is likely the source of a disease outbreak in the provided case study.
Step-by-step explanation:
Based on the case presented, the food item that should not be served at the nursing home's barbecue for its residents is the chicken salad. In the reference case, all who consumed the chicken salad, except two vegetarian students, developed symptoms of food poisoning such as nausea, vomiting, abdominal cramps, and in one case, signs of shock due to low blood pressure. The fact that only those who ate the chicken salad got sick and the vegetarians did not points to the chicken salad as the likely source of the disease outbreak.