I presume that the sample size n = 250 and the proportion with the disease in this sample is 34%.

the interpretation is that the probability that the true population proportion will lie between 28.25% and 39.8% is 0.95.

The first question is whether this is a point prevalence or a period prevalence.

A point prevalence is the proportion of the population who have the problem at a point in time. It is useful for conditions that don't fluctuate in the short term, such as obesity, cancer etc.

The period prevalence is the proportion of the population who have experienced the problem in a given time window – in the case of diarrhoea, it could be one or more episodes in the past week, or the past month. Given my work in diarrhoeal disease, the prevalence you give looks more like a period prevalence, which is why I mention it.

I am presuming that when you say prevalence, you are not looking at the proportion of people who develop the condition in a defined period of time (cumulative incidence) or the number of events per unit of population per unit of time (incidence density). Incidence density is the best measure of diarrhoeal disease because children especially will have multiple episodes, and each episode increases risk to health, so the aim of intervention is to reduce the episode rate, not to reduce the proportion of children who experience one or more episodes.

Hi

I believe James Leigh gave the right answer for the question given the information contained in the question.

Thanks

Thank you very much for the feedback.

Prevalence rate is the number of all existing cases ( old &new) at specific place and time/ total population at that time and space * 100’

The confidence interval (CI) can't be interpreted in terms of probability (that's only possible in a Bayesian frame): in front of a CI we can only say that we are very confident (we have a confidence of 95%) that this interval contains the true population parameter, in this case, the prevalence (%). But, "confidence" is not "probability"

While the understanding of the implication is necessary, I guess the interpretation given by James Leigh best describes the situation.

I very much agree with both Ronan Michael Conry and James Leigh.

James Leigh's answer is wrong. We can never interpret a confidence interval (CI) in probabilistic terms.

Patricio is technically correct. More exactly the interpertation should be that the statement that the population proportion (not a random variable) lies between P +/- 1.96 SE(P) will be true in 95% of repeated samples of the same size.

It is in this sense that one should interpret "probability ' in my earlier answer.

however this explanation is somewhat harder to grasp for many

James Leigh – indeed, it is nonsensical since it refers to worlds which do not and cannot exist. I have data on 24 rare cancers (the sum total of cases from two national treatment centres). So the confidence interval is telling me that if I ran my study repeatedly… but wait – these are all the cases there are. If we sampled from other countries or other time periods, we would be sampling different populations. So the definition of a confidence interval seems to imply something like parallel universes.

Patricio Suárez-Gil – frequentists will say that with a particular sample, the true value is either in it or not, the probability is zero or one. But you might say that about a lottery ticket, or when you are evaluating the clinical risk of a patient.

So why cannot we see a confidence interval like a (lucky) lottery ticket, such that 95% of tickets contain a prize?

James, that interpretation is technically incorrect. As the population proportion isn't a random variable, you can't do probabilistic statements. You only can affirm that you are very confident that your confidence interval is one of those that contains the parameter (a fixed value).