 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-4/17h/d/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Averaging the centered model gives

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

Therefore

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

z_{0.975} = Φ^{- 1} (0.975)

, an exact 95% confidence interval is

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

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