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.

My thought:

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??


Your statement is false because of the part of the sentence that said " $95\text{%}$ of them would have the mean between $(25,50)$". The true statement should be "...$95\text{%}$ of them would contain the true population mean $\mu$. It could be that none of the sample mean is between $25$ and $50$ but the confident interval still contains $\mu$.

  • $\begingroup$ Thank you for your comment. Is my thought a bit away from what you wrote? $\endgroup$ – user2791 Oct 24 '14 at 0:14
  • $\begingroup$ May I ask which part is wrong? Actually, the first box is the false statement and the second box is my whole thought. $\endgroup$ – user2791 Oct 24 '14 at 0:42
  • $\begingroup$ Because I use "true population parameter" instead of "true population mean"? $\endgroup$ – user2791 Oct 24 '14 at 0:46
  • $\begingroup$ No. The wrong part is the $(25,50)$ interval. The C.I invertal can vary for each sample. $\endgroup$ – DeepSea Oct 24 '14 at 0:59
  • $\begingroup$ Oh I understand what you meant. Thanks! $\endgroup$ – user2791 Oct 24 '14 at 1:10

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