 However, at least in Lindley's example, if we take a sequence of significance levels, , such that with , then the posterior probability of the null converges to 0, which is consistent with a rejection of the null.In this numerical example, taking , results in a significance level of 0.00318, so the frequentist would not reject the null hypothesis, which is roughly in agreement with the Bayesian approach.If we use an uninformative prior and test a hypothesis more similar to that in the frequentist approach, the paradox disappears.