## Sample size required to estimate means dependent samples

Sample Size to estimate means(paired) | ||
---|---|---|

Confidence Level ($1-\alpha$) | ||

Standard Deviation ($\sigma_d$) | ||

Margin of Error ($E$) | ||

Results | ||

Z value: | ||

Required Sample Size : ($n$) | ||

## Sample size required to estimate difference between means of dependent samples

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

```
$$
n =\bigg(\frac{z\sigma_d}{E}\bigg)^2
$$
```

where

- $n$ is the sample size,
- $z$ is the $Z_{\alpha/2}$,
- $\sigma_d$ is the population standard deviation of the difference and
- $E$ is the margin of error.