Final answer:
The study design described is a case-control study, which retrospectively compares the exposure to high dust lead levels in homes among children with lead poisoning (cases) to those without (controls).
Step-by-step explanation:
The study design in question is a case-control study. This type of study compares a group of individuals with a disease or outcome of interest (cases) to a group without the disease or outcome (controls), looking retrospectively to compare how frequently the exposure to a risk factor is present in each group to determine the relationship between the risk factor and the disease.
In this particular scenario, the risk factor is high dust lead levels in homes, and the disease outcome is lead poisoning in children. There were 200 cases of lead poisoning, 50 of which had high dust lead levels, and 200 controls, 30 of which had high dust lead levels. These findings are indicative of exposure to lead as a risk factor for lead poisoning.