= Solution
At level $0.05$ the two-sided critical values are $\pm1.96$. Since $|-1.89|<1.96$, \b[do not reject the two-sided null]. The approximate two-sided $p$-value is $2\Phi(-1.89)\approx0.059$.
For the specified alternative $q>p$, the statistic $\hat p-\hat q$ should be negative. Reject in the lower tail, $Z<-1.64$. Since $-1.89<-1.64$, \b[reject for this one-sided alternative], with approximate $p$-value $\Phi(-1.89)\approx0.029$. The direction of the tail follows the order of subtraction in the statistic.
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