# CI for two populations

The heights (in) for non-Hispanic white females in 2008 was the following:

Age      Sample Size        Sample Mean        Std Error
20-39    866                64.9               0.09
60+      934                63.1               0.11

Calculate and interpret a CI at confidence level 95% for the difference between population mean height of the younger women and that for the older women.


Does the above question use the following formula to get the correct answer?

$p1 - p2 \stackrel{+}{-} z \sqrt{ \frac{s1^2}{n1} + \frac{s2^2}{n2} }$

where:

p1 = 64.9     s1 = 0.09
p2 = 63.1     s2 = 0.11
z = 1.96
n1 = 866
n2 = 934


you have forgotten the z. And you have here given the means not the $p_i´s$ So the limits of the CI are $\overline{x_1}-\overline{x_2}\pm z_{0.95}\cdot \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$
Here it is allowed to take the normal Distribution, because $n_1$ and $n_2$ are both greater than 30 (approximation). In general the differences are student t-distributed.