Suppose that someone proposes a new way to calculate a 95% confidence interval for a mean. This could involve any arithmetic on the given data.
For example, it could say to go out 1.75 interquartile ranges (IQRs) on either side of the median.
What would it mean to say that this procedure produces valid 95% confidence intervals?
How could you use simulation to check whether the procedure produces valid 95% confidence intervals?