I have this statement:
If a 95% confidence interval for the mean was computed as (25,50), then if several more samples were taken with the same sample size, then 95% of them would have a sample mean between (25,50)
And I know this statement is false, but I want to know exactly why.
If several more samples were taken with the same sample size, and created a confidence interval from each statistic, over the long run 95% confidence interval; (25,50) will contain the true population parameter (should I say true population mean?), not a sample mean.
For example, if we take 100 different samples and compute 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value.
Any better idea??