Past exam of the probability, statistics and options I course of the University of Oxford / 2011 / O / 3 / c / Solution

Under $H_0:\mu =0$, the statistic $T=\sqrt{n}\overline{X}/S$ has Student t-distribution with $n-1$ degrees of freedom. Reject in either tail, splitting the null error probability equally. Thus the critical region isThe distribution is continuous, so the boundary convention does not change the size $\alpha$.