Question

Notation What does the notation $Z_{\alpha }$ indicate?

Short answer

$z_{\alpha }$ indicates a critical value on a standard normal curve with a right-side area equal to .

Step-by-step solution

Given information

An expression for critical value is given.

Identify the notation

The value $z_{\alpha }$denotes a specific z-score value with an area equivalent to the measure (significance level) on its right on the standard normal curve.

The measure of significance will never fall beyond 0 and 1.

It is often recognized as a critical value with measure $\alpha$.

Mathematically,

$$\begin{gathered} \text{Area}\text{to}\text{the}\text{right}\text{of}{z}_{\alpha }=P\left(Z>z_{\alpha }\right) \\ =\alpha \end{gathered}$$

For example, for $\alpha =0.05$,$z_{0.05}$ is a point on a standard normal curve such that area to the right of the point is 0.05.