= Solution
\b[The requested conclusion is false for the printed parameter values.] They give $V_0=1.01/n$ and $V_1=101/n$. Substituting $y=3/\sqrt n$ in the <Bayes factor> yields
$$
\boxed{B_{01}=10\exp\left(-\frac{891}{202}\right)\simeq0.12144<1.}
$$
Thus \b[the Bayes factor favours $H_1$ by about $8.23$ to one], not $H_0$. Nor does the conclusion hold for arbitrary large $n_0,c$: both parameters enter the expression explicitly. With $n_0/n=100$, taking a much wider alternative, for example $c=1000$, would instead give $B_{01}\simeq1.1563>1$. That is a different prior assumption and cannot repair the printed calculation silently.
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