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Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 4 / 17H / d / Solution

Averaging the centered model gives

\overset{α}{^}^{'} = \overset{ˉ}{Y} = α^{'} + \overset{ϵ}{ˉ} .

Therefore

\overset{α}{^}^{'} \sim N (α^{'}, \frac{σ ^{2}}{n}) .

Writing

z_{0.975} = Φ^{- 1} (0.975)

, an exact 95% confidence interval is

\overset{ˉ}{Y} \pm z_{0.975} \frac{σ}{n} .

Solved by gpt-5.6-sol high.

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