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Here's my simple words-only description of a 95% confidence interval for the mean. How accurate is it?

  • the sample mean comes from a distribution of possible sample means
  • the sample mean might have been drawn from anywhere in the distribution of sample means
  • worst case scenario is that the sample mean was drawn either from the extreme left hand or extreme right hand of the distribution of sample means
  • these two extremes mark the boundaries of the confidence interval
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    $\begingroup$ Have you read the answers at stats.stackexchange.com/questions/26450? Or at stats.stackexchange.com/questions/2272? They fully address your question. Incidentally, many people use models in which the sample is viewed as drawn from some Normal distribution. There is no worst case scenario, because no matter what the sample mean may be, it's always possible it could have been smaller by $1$ or larger by $1$, so your two extremes are $-\infty$ and $+\infty$. $\endgroup$ – whuber Jun 17 '15 at 18:31
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If you re-sample 100 times and calculate an interval estimate each time, then 95 of those intervals will contain the "true" mean.

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    $\begingroup$ Please be clearer: from what are you resampling? The parent distribution or the sample itself? And didn't you mean to preface this statement by "on average"? $\endgroup$ – whuber Jun 17 '15 at 18:34

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