## Confidence Limits for Population Means

### To calculate confidence limits for population means

You can calculate a pooled variance as:

$$s^2_p = \frac{df_1 s^2_1 + df_2 s^2_2}{df_1 + df_2}$$

Confidence limits for population means

You can calculate this with:

$$\bar{x} \pm t_{\alpha (2), df} \sqrt{\frac{s^2_p}{n}}$$

where Xi is the mean of each population, ta(2),v is the t value for the confidence range,  with a(2) significance and v degrees of freedom.   The variance is the pooled variance from above and n is the number of samples taken.

Also See:

Chapter 9 - Two-Sample Hypotheses pages 130-132 in:

Zar, J. H. 2007. Biostatistical Analysis. Prentice-Hall, Inc. Englewood Cliffs, New Jersey. 718 pp.