# Prove property of a confidence interval

How does one go about proving the characteristic of a confidence interval that:

A 95% confidence interval means if you were to randomly sample the same way 1000 times and create 1000 confidence intervals, approximately 95% of these intervals would contain the true parameter.

A confidence interval is calculated using the sample mean and the standard error so each confidence interval will be different (unique to the sample), and people talk about how to interpret the confidence interval (as above), but how does one go about proving that indeed 95% of these intervals would contain the true parameter/mean?

Thanks

• If the interval had the correct (95%) coverage, you would not generally get 950 in 1000 intervals containing the parameter -- in fact you'd only see 950 about 6% of the time, and you could easily get below 940 or above 960. – Glen_b Mar 10 '19 at 10:53