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Statistical Power and sample sizePredicting Ztest statistical power Estimating required sample size for a ZtestPredicting statistical power for the ZtestOnetailed testTwotailed test
Clearly if we only took four samples, our test would have very little power to reject the null hypothesis. The question then is how many samples would be required to give us a reasonable chance (say 80%) of rejecting the null hypothesis. We could use repeated estimates of the power for different sample sizes to produce a power curve: The required number of samples for a power of 80% could then be read of the graph  in this case we would need around 20 samples. But it would be a lot easier to rearrange the equation, and estimate the required number of samples directly.
Estimating required sample size for the ZtestOnetailed test
Twotailed testSample size calculations for a twotailed test are identical except that you use the z values at α/2 instead of α.
