Appropriateness of p-value in my data

Our study examined whether there would be a change in prescription rates following an intervention. We had 236 patients. 109 before intervention & 127 after the intervention. We were interested in subgroups. Because we were interested in rates, we used simple difference in population statistics and generated p-values/CI's for each of our subgroups. These formulas take n into account, but I read that there may be certain assumptions about the size of the sample and the appropriateness of the p-value. I don't know what those assumptions are. Any insight into a) if the p-value is appropriate given our small subgroups, b) if a one-tailed or two-tailed z test was appropriate. Thanks in advance.

A 2 tail test is usual except in special situations, so p = 0.032 is appropriate.
This would commonly be done with a chi square test which gives p = 0.032 as well.
It looks like your analysis program included the continuity correction (since I get 0.017 one tailed using continuity corrected chi-square). You may want to see if you need to use that stricter version, based on the expected cell frequencies. The uncorrected chi-square gives a smaller p value. // I agree that either should be two-tailed (i.e., double the one-tailed p value) since the rate could have gone up or down. If your intervention could not plausibly have increased the rate, you could argue for a one-tailed test. that's judgment.// By the way, each patient is counted exactly once, right? 12 prescriptions means that 12 patients had a prescription? If it could have been 8 patients, some of whom had two prescriptions, the z test for percentages (or the equivalent chi-square) are both inappropriate.