A common misconception is that a confidence interval is two values that you are 95% sure that the true value of the parameter you are estimating is between. An x% confidence interval is actually the results of an equation that x% of the time, using data drawn from an underlying population returns a range containing the true parameter of interest.
Each line in this visualization is a 95% confidence interval of a draw from a binomially distributed population with n = 100. For more info on the process see the sister visualization Binomially Distributed Fun!
Choose the probability of success (theta) for your binomial draw:
Note how when the selected theta is close to 0 or 1 the true coverage % of the interval changes.
The more simulations you run the closer the observed coverage percentange is to the true coverage of the interval. This may not be 95%.
|True coverage %:||56%|