Confidence interval for a proportion in a small sample

Hi everyone! I am new here, trying to get some opinions on a strange article I came upon. So it shows results of a small survey, on a sample of 24 subjects. The thing that is weird to me that the proportion of certain answers is also expressed as a confidence interval. The example is shown below. Am I right that this does not really make sense?
Thank you for your help!


Less is more. Stay pure. Stay poor.
Well, say the question was, what type of insurance do you have (I.e., private, federal, state, None). Yeah these would be OK, but not great. So, 54% have private insurance but in random resampling of the source population the true value would be within 35% and 73% about 95% of the time.

Does this help? P.S., I didn't check their math, but the CI on the count of two seems kind of narrow, but could be fine. Also, there are no % outside of 0-100% range which is good, meaning they may have used the right formula.

Welcome to the forum!
OK, thank you for the answer, it helped! I have just never seen the results expressed like this (these are actually the results of a knowledge test) when you have a really small sample, but I do understand now that it can still be valid.