# Computing type II error $\beta$ [closed]

In hypothesis testing for the value of the population mean, when computing type II error $\beta$, if the alternative hypothesis includes many possibilities, is it always the case that $\beta$ is approximated? In other words, when we compute a numerical value for $\beta$, based on the mean from the sample $\bar{X}$, shouldn't we write $\beta \approx P[\text{do not reject } H_0 \mid \mu = \bar{X} ]$?

If there is no other information available, of course, it's the only way to compute $\beta$. It's the best we can do. But since $\bar{X}$ may very well not be $\mu$, shouldn't it be stressed that it's $\approx$ and not $=$?

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[crickets...] try stats.stackexchange.com – user53153 Feb 17 at 1:51
Thanks for the suggestion... Done: stats.stackexchange.com/questions/50177/… – Gene Arboit Feb 17 at 13:36
Can this be migrated to Stats SE? Regards – Amzoti Feb 17 at 18:11
I just put in a request for doing so (flag > ...) – Gene Arboit Feb 17 at 18:12

## closed as off topic by Micah, ncmathsadist, Davide Giraudo, Henry T. Horton, tomaszFeb 17 at 19:12

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