# Symbols and naming in confidence interval

Suppose to have a confidence interval for the mean on a large sample, i.e.

$$\overline{X}-z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}} \le \mu \le \overline{X}+z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$$

Exists any common used symbol to address the $z_{\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt{n}}$ term? Any reference is appreciated.

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In our book they use $z_{\frac {a}{2}}$ for the 1.96 term with $a$ being the $100-a$% confidence interval so in this case we would have$z_{2.5}$ – Ben Feb 13 '13 at 15:05
Yes you are right! I should be more formal. A 95% confidence level is a classic and I supposed a large sample so that T-student must not be used. I will edit the question, but the problem remains. – Roberto Trunfio Feb 13 '13 at 16:12

I found here that $z_{\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt{n}}$ is named "margin of error m".
For what it's worth: The term $\frac{\sigma}{\sqrt{n}}$ is called the standard error of the estimator $\bar{X}$, and is often denoted by $\mathrm{SE}(\bar{X})$. Hence your confidence interval can be written $$\bar{X}-z_{\alpha/2}\mathrm{SE}(\bar{X})\leq \mu\leq \bar{X}+z_{\alpha/2}\mathrm{SE}(\bar{X}).$$
Unfortunately, I have never heard the term margin of error before (though I guess it would make sense to call it that). But I think this is the most common and compact way to write a confidence interval. Note that the significance level $\alpha$ only appears in $z_{\alpha/2}$ and that the things we observe only appears in the (estimated) standard error. So if we were to recalculate a different confidence interval, we need only to recalculate $z_{\alpha/2}$. That is why this is a smart way of writing it. – Stefan Hansen Feb 14 '13 at 14:25
Good point. However, one can write $m_\alpha$ too. Moreover, some data is missing also from the use of the sample mean $\overline{X}$, e.g. the sample size. – Roberto Trunfio Feb 14 '13 at 16:31