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.
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Author: Dr. David R. Larsen
Created: August 17, 1998
Last Updated: December 12, 2019