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

Use the residual variance estimatorUnder the Gaussian linear model, $\bar{Y}$ is independent of $s^2$ andConsequently the Student t confidence interval for a centered regression intercept follows fromIt isThe displayed pivotal quantity lies between its 2.5% and 97.5% quantiles with probability $0.95$, which proves the stated coverage.