= 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.
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