When calculating a confidence interval for a proportion, you should keep the following in mind:
In practice, we may trust this confidence interval when the number of successes is $15$ or greater and
the number of failures is $15$ or greater. That is,
when $np_0 \geq 15$ and $n(1 - p_0) \geq 15$.
The confidence levels can be inaccurate unless your sample size sample is large.
The actual confidence level can be less than the confidence level you specify.
This page also computes the "plus four" interval.
Statistical literature suggests that the plus four interval yields better results
than the usual large-sample interval.
Experts in statistical practice recommend that you use the
plus four interval for estimating a proportion when
the confidence level at least $90\%$ and the sample size is at least $10.$