Critical values (z*-values) are an important component of confidence intervals (the statistical technique for estimating population parameters). The z*-value, which appears in the margin of error formula, measures the number of standard errors to be added and subtracted in order to achieve your desired confidence level (the percentage confidence you want).
The following table shows common confidence levels and their corresponding z*-values.
| Confidence Level | z*-value |
|---|---|
| 80% | 1.28 |
| 85% | 1.44 |
| 90% | 1.645 |
| 95% | 1.96 |
| 98% | 2.33 |
| 99% | 2.58 |
You can also use these critical z*-values for hypothesis tests in which the test statistic follows a Z-distribution. If the absolute value of the test statistic is greater than the corresponding z*-value, then reject the null hypothesis.
