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The critical region, determined by the significance level α, is the set of values that will lead to rejecting the null hypothesis H_0. In a standard normal distribution, this region is located in the tails of the distribution. The cutoff value of the region is a critical value given by the z-value of α. The tests of significance — left, right, or two-tail — determine whether there are one or two critical regions.
| Critical Values | |||
|---|---|---|---|
| Significance Level | Left-Tail Test H_a:μ | Two-Tail Test H_a:μ≠ k |
Right-Tail Test H_a:μ>k |
| α=1 % | -2.326 | ±2.576 | 2.326 |
| α=5 % | -1.645 | ±1.960 | 1.645 |
| α=10 % | -1.282 | ±1.645 | 1.282 |
This table shows the typical significance levels and their corresponding critical values. It is worth noting that the area of the critical region(s) is equal to the significance level α.
