Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 221 / 4 / a / Solution

Restricting to pupils who already attended a Catholic middle school improves covariate balance: the treatment-group differences in family income, urban residence, and prior mathematics score are all much smaller. This makes severe extrapolation and measured confounding less prominent.

The restriction reduces the sample from $11,839$ to $1,006$, so estimates are less precise. It also changes the target population to Catholic-middle-school pupils, reducing external validity for all United States pupils.