Confidence interval for a proportion in a small sample

[tamina]

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!

 

[hlsmith]

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!

 

[tamina]

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.