Usually, people tend to confuse the interpretation of confidence intervals. The following two statements are said to be quite confusing (even to myself):
- A 95% Confidence Interval means that the population parameter will be contained within this interval with a probability of 0.95 (incorrect)
- A 95% Confidence Interval means that the Confidence Interval itself has a 0.95 probability of containing the population parameter (less incorrect)
I was wondering if it is possible to create some example (e.g., an R simulation) which shows that why one of the above statements is more correct than the other.
I found this post here The importance of a correct interpretation of a confidence interval in which R code is provided that simulates data to illustrate these concepts.
But is it possible to create an example in which it becomes clear that interpreting a confidence interval as "the probability of the population parameter being contained within this interval" is clearly incorrect or results in a contradiction?
Perhaps someone can think of such an example or provide a link/reference to such an example?