Let $Y_s(1)$ and $Y_s(0)$ be the <potential outcomes> for the apprenticeship proportion at school $s$ if it is or is not converted to a UTC. The policy-relevant estimand is the average causal effect
$$
\mathbb E\{Y_s(1)-Y_s(0)\}
$$
over the population of schools eligible for conversion. Ideally this would be identified by a <Randomized controlled trial> of conversion, or by an observational design that reproduces its exchangeability.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 207 / 1 / a / Solution

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Random treatment assignment makes treatment independent of baseline potential outcomes in expectation.


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