Overview of Confidence Intervals

All the confidence intervals follow a pattern

ESTIMATE $\pm$ CRITICAL VALUE * (SE of ESTIMATE)

The following summary table lists the ESTIMATES and corresponding SE's. The CRITICAL VALUE is simply a multiplier that fine tunes the length of the confidence interval according to the desired level of confidence. The exact value of the critical value is read from the t or z curve (but roughly speaking, a value close to 1 gives a 68% level of confidence while a value close to 2 gives a 95% level of confidence).

ESTIMATE	SE OF ESTIMATE	CRITICAL VALUE
$\overline{X}$	$S/\sqrt {n}$	t (df=n-1)
$\overline{X}_1-\overline{X}_2$	$\sqrt{ \mbox{SE}_1^2 + \mbox{SE}_2^2}$ where
	if $\mbox{SE}_1=S_1/\sqrt{n_1}$, $\mbox{SE}_2=S_2/\sqrt{n_2}$	then z
	if $\mbox{SE}_1=S_p/\sqrt{n_1}$, $\mbox{SE}_2=S_p/\sqrt{n_2}$	then t (df=n1+n2-2)
$\hat{p}$	$\frac{\sqrt{\hat{p}(1-\hat{p})}}{\sqrt{n}}$	z
$\hat{p_1}-\hat{p_2}$	$\sqrt{ \mbox{SE}_1^2 + \mbox{SE}_2^2}$ where
	$\;\;\; \mbox{SE}_1=\frac{\sqrt{\hat{p}_1(1-\hat{p}_1)}}{\sqrt{n_1}}$, $\mbox{SE}_2=\frac{\sqrt{\hat{p}_2(1-\hat{p}_2)}}{\sqrt{n_2}}$	z