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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??

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1 Answer 1

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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 $\mu$.

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  • $\begingroup$ Thank you for your comment. Is my thought a bit away from what you wrote? $\endgroup$
    – user2791
    Oct 24, 2014 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, 2014 at 0:42
  • $\begingroup$ Because I use "true population parameter" instead of "true population mean"? $\endgroup$
    – user2791
    Oct 24, 2014 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, 2014 at 0:59
  • $\begingroup$ Oh I understand what you meant. Thanks! $\endgroup$
    – user2791
    Oct 24, 2014 at 1:10

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