Sample size estimates for means in two independent samples

The formula to estimate the sample size required to estimate the mean of two independent samples is

$$ n_i =2\bigg(\frac{z\sigma}{E}\bigg)^2; i=1,2 $$


  • $n_i$ is the sample size for $i^{th}$ group,
  • $z$ is the $Z_{\alpha/2}$,
  • $\sigma$ is the population standard deviation and
  • $E$ is the margin of error.

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