The most effective claim for Cleo's argument is:
Kennedy High School should open at 8:30 a.m. instead of 7:30 because students would get an extra hour of sleep, improving their health and brain function.
This claim is strong because it directly addresses a key benefit of starting school later: the positive impact on students' health and cognitive function, which is supported by research on sleep and academic performance. It presents a clear, specific, and compelling reason for the proposed change, which is likely to resonate with both stakeholders and decision-makers at the school.