8.1 A single population mean using the normal distribution  (Page 6/20)

The error bound formula for a population mean when the population standard deviation is known is
EBM = $\left(z_{\frac{\alpha }{2}}\right)\left(\frac{\sigma }{\sqrt{n}}\right)$ .

The formula for sample size is n = $\frac{z^2{\sigma }^2}{EB{M}^2}$ , found by solving the error bound formula for n .

In this formula, z is $z_{\frac{\alpha }{2}}$ , corresponding to the desired confidence level. A researcher planning a study who wants a specified confidence level and error bound can use this formula to calculate the size of the sample needed for the study.

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