Suppose there is a population, with goods and bads. The bad rate of the population(=bads/(bads+goods)) is of course unknown.
Now, I have a sample of $N$ from the population and I know the bad rate of this sample as $b$. The question is can I calculate the confidence interval based on $N$ and $b$ ONLY? In other words, can I calculate the confidence interval $x$ such that with, say, 95% confidence the population bad rate falls in $[\text{range}_1,\text{range}_2]$, where $\text{range}_1$ will be $b-x$ and $\text{range}_2$ will be $b+x$.