For a hypothesis test on the population proportion, we always look up the z-table to find the critical values. If that's a one-tailed test, the area of the region at the end tail would be alpha, the significance level. But if that's a two-tailed test, the area of the region at the end tail would be alpha/2.
In this case, alpha = 0.01 as given. So we'll look up the z-table with alpha = 0.01. That would give us a critical value of 2.3263.
So the answer is 2.3263.