It is a relatively small sample with only 24 observations (there is a total of 32 observations there, but 8 people haven't attended loud events, so they don't count). You will be surprised to find out that statisticians would refer to a sample with 30 or more observations as a "large sample:"
"
...at least when large samples are used, such as N ≥ 30."
We are trying to estimate population proportion. Condition 3 on page 106 of
https://projecteuclid.org/download/pdf_1/euclid.ss/1009213286
states that confidence intervals may be used if n*p_hat>5, where p_hat is the sample proportion (in our case the proportion in our sample who got a permanent spike). According to the paper above, condition 3 is a statement that can be found in some popular stats textbooks. In our case n*p_hat = 24*8/24 = 8>5. The paper goes on to critisize this condition. I will come back to their critique momentarily. If that condition 3 is true, then we can use the confidence interval calculators on
http://www.sample-size.net/confidence-interval-proportion/
I set N = 24, x = 8, and CL = 99. I am looking for a 99% confidence interval. The online calculator is providing us with two sets of confidence intervals. One is
Lower bound = 0.119
Upper bound = 0.614
The other one is
Lower bound = P - (Zα*SEM) = 0.085
Upper bound = P + (Zα*SEM) = 0.581
The above are 99% confidence intervals. For an interpretation of the meaning of a confidence interval, see
http://www.mathbootcamps.com/interpreting-confidence-intervals/
To paraphrase, 99% of the time, the TRUE population proportion (of the fraction of people who will get a Permanent spike after attending a noisy event) will be between 8.5% and 58% (I am using the second interval above). 1% of the time, it will not. We are 99% confident that the fraction of tinnitus sufferers who will get a permanent spike after attending a loud event is between 8.5% and 58%. This statement takes the sample size into account. As a result of that relatively small sample size, we ended up with a 99% confidence interval that is wider.