What does z* represent in statistics? Could somebody please give me an explanation as to what Z-star means for statistics, where it's used, and how to calculate it?  My book is very confusing and I don't really know what it means.  Even a link to a website would be helpful.
Main questions I need to answer:
What does $z^{∗}$ represent? What is the value of $z^{∗}$ for a 95% and 90% confidence interval? Include a sketch.
Thank you very much.
 A: It means the "critical value of $z$."
This is taken from wikipedia:

In statistics, z* and t* are given critical points for z-distributions
  and t-distributions, respectively.



I appreciate it but that doesn't really help as I have a huge
  background in calculus where a "critical point" probably has a totally
  different meaning. Maybe an example problem and answer?

Certainly. In hypothesis testing, e.g. comparing a mean to a fixed number, we used the data to generate a z-statistics, and then we will see if that z-value is at the extreme tails of a normal distribution that is based on the premise that the null hypothesis is true. If the observed z-value is more extreme than that "critical value," we will reject the null hypothesis.
The critical value depends on your preset type I error rate. Most of the time it's 5% (corresponding to a 95% confidence interval), and we will then make the left and right side 2.5% area under the normal distribution our "rejection zone." The value that defines the starting of that rejection zone is the critical value.
For instance, in a two-tailed test, the critical value for 95% is 1.96 (which means if your observed z-score is bigger than 1.96 or smaller than -1.96 you'll reject the null.) For one-tailed, it'd be 1.64 at the right OR -1.64 at the left.
A: z* means the critical value of z to provide region of rejection
if confidence level is 99%, z* = 2.576
if confidence level is 95%, z* = 1.960
if confidence level is 90%, z* = 1.645
