Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 3 / 18H / d / ii / Solution

For large $|\overline{x}|$, the supplied normal-tail approximation givesMeanwhile,Since $5000/101<50$, the posterior point-null probability decays more slowly. Therefore, for sufficiently large $|\overline{x}|$,This reversal is the Jeffreys-Lindley paradox for a Gaussian point null.