Critical Value z* for z-Scores for Confidence Levels

confidence level

0.9

This Demonstration explains how a

*

z

-score (a critical

z

-score) is related to confidence levels and used for the traditional method of significance tests [1]. As you move the slider, the confidence level changes, and in turn the area as well as the

*

z

-score changes.

The critical value

*

z

is calculated by using a confidence level and finding the tail area of one side, and then taking the inverse of the cumulative distribution function of that area to get

*

z

. A confidence interval is a range that is calculated using the sample mean and the population standard deviation. If many samples are taken and many intervals are created,

x%

of the resulting intervals will contain the true population mean, where

x

is the chosen confidence level (for example, 99%).