Say I have a sample population A it has mean $\mu_A$. I sample A and obtain another sample population $\hat A$, it has a mean of $\mu_\hat A$.

If a hypothesis test indicates that I should be 95% confident that the two means $\mu_A$ and $\mu_\hat A$ are not equal.

What can I infer about $\hat A$ ?
How might it be different from A.

  • $\begingroup$ You might want to rethink how you describe the hypothesis test. You probably mean "There is a 0.05 or less probability that if the two means were equal we would see the data we did", which is not the same? $\endgroup$ – Peter Ellis Feb 8 '18 at 1:30
  • $\begingroup$ @PeterEllis I am saying that 95% of the time I expect the difference in the means not be equal to 0. Is that not what I wrote? $\endgroup$ – grldsndrs Feb 8 '18 at 1:48

You seem to be describing the procedure of the bootstrap which allows you to estimate the standard deviation of a measured statistics (in your case the mean of the series) by sampling the series many times with replacements.

By performing bootstraping you will be able to infer the distribution of μA (it's standard deviation, or any of it's relevant CI).

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  • $\begingroup$ Ok this'll give a framework to think about it, but I'm still having trouble fleshing out the implications. Care to speculate? $\endgroup$ – grldsndrs Feb 12 '18 at 20:32
  • $\begingroup$ Can you explain what you are looking for? What would you like to learn about population A? and it's μA? $\endgroup$ – ShaharA Feb 13 '18 at 9:25

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