## Sample size to test mean

Use this calculator to find the minimum sample size required to test mean $\mu$.

Sample Size to test mean
Confidence Level ($1-\alpha$)
Power ($1-\beta$)
Mean under H0 : ($\mu_0$)
Mean under H1 : ($\mu_1$)
Standard Deviation ($\sigma$)
Results
Effect Size ($ES$)
Z value: $Z_{1-\alpha/2}$
Z value: $Z_{1-\beta}$
Required Sample Size : ($n$)

## Sample size to test mean

The $ES$ is defined as $$ES=\frac{|\mu_1-\mu_0|}{\sigma}$$

where $\mu_0$ is the mean under $H_0$ and $\mu_1$ is the mean under $H_1$, $\sigma$ is the standard deviation.

The formula for determining the sample size required to ensure that the test has a specified power is $$n =\bigg(\frac{Z_{1-\alpha/2}+Z_{1-\beta}}{ES}\bigg)^2$$

where

• $\alpha$ is the selected level of significance,
• $1-\beta$ is the selected power and
• $ES$ is the effect size.