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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
 




2003-09-08