I need some help with statistics

Let's say that I'm trying to determine the percentage of left-handed people and I want to determine it solely based on a statistic I've made - I went to a school and asked 23 people if they were left-handed, and just 2 of them said they were, the rest said they were right-handed. For some reason, I'm certain the 2 were really left-handed, but someone of the 21 might have been left-handed and misunderstood the question and told me he's right-handed instead (the chance for that is small, you might ignore it if you find it hard to take it into account).

Obviously, the best guess would be that one out of 11.5 (2/23) is left-handed. However, I need to know an interval (let's say 4%-44%, those are just random numbers to describe an example of an interval), so that the real number of left-handed people is most likely somewhere in the interval (with 5% chance of them not being in the interval). If a piece of information is missing, feel free to make assumptions that make sense (at least as much as possible), as long as you explain them after that. Also, I need the method of calculation, because I'd need to apply it to different numbers.