Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 35 / 3 / d / Solution

Divide the two normal distribution predictive densities to obtain the Bayes factorAt $y=0$ this becomesThe wider prior distribution spreads its predictive mass over more possible means, giving the narrower model more Bayesian model evidence for observations very near zero. Away from zero, the exponential term opposes that factor.