Significance Level(α)：
The Type of Test：
One Tailed
Two Tailed
z score result
The Z critical value is the boundary value that separates the rejection region from the acceptance region in the standard normal distribution. It is used in hypothesis testing and confidence interval calculation. Its value is determined by the significance level α and the type of test (one-tailed/two-tailed).
The significance level, usually denoted as α, is the maximum acceptable probability of making a Type I error (i.e., a false positive error, which occurs when the null hypothesis is incorrectly rejected when it is actually true) in hypothesis testing. Common significance levels include 0.10, 0.05, and 0.01. The significance level is closely related to the confidence level, where the confidence level is calculated as 1−α1−α. For example, when the significance level α=0.05, the corresponding confidence level is 95%.
Steps to Calculate the z Critical Value:
Step1：Determine the Significance Level
First, you need to determine the significance level (α), which is typically 0.05 or 0.01.If the confidence level is known, the significance level can be calculated using the formula: significance level(α)=1-confidence level
Step2：Look Up the z Table
Based on the significance level, look up the critical value in the standard normal distribution table (z table).
One-Tailed Test:
If it is a one-tailed test, the z critical value corresponds to the cumulative distribution function value of 1−α.Two-Tailed Test:
If it is a two-tailed test, the z critical value corresponds to the cumulative distribution function value of 1−α/2.For a two-tailed test with a significance level of 0.05, you look for the z value of 0.975, which is typically 1.96.
For a one-tailed test with a significance level of 0.05, you look for the z value of 0.95, which is typically 1.645.
| Confidence Level | Two-tailed Critical Value | One-tailed Critical Value |
|---|---|---|
| 90% | ±1.645 | 1.282 |
| 95% | ±1.960 | 1.645 |
| 99% | ±2.576 | 2.326 |
| 99.9% | ±3.291 | 3.090 |
source from: z score table
