Final answer:
The critical values zα or zα/2 designate the rejection region's boundary in hypothesis testing, with α - representing the level of significance. These values are determined using a standard normal probability table and vary depending on whether the test is one-tailed or two-tailed.
Step-by-step explanation:
The critical values zα or zα/2 are the boundary values for the rejection region(s). The level of significance, denoted by α (alpha), corresponds to the probability of committing a Type I error, which is rejecting the null hypothesis when it is indeed true. The critical value zα corresponds to a one-tailed test, while zα/2 applies to a two-tailed test. In the context of a standard normal distribution, these z-scores represent the cutoff points beyond which we would consider the test statistics to be significant enough to reject the null hypothesis.
For example, assuming a confidence level (CL) of 95%, the level of significance will be 5% (α = 0.05). This α is split between the two tails of the distribution in a two-tailed test, with each tail containing 2.5% (α/2 = 0.025). Using a standard normal probability table, we find that the z-score corresponding to an area to the right of 0.025 is approximately 1.96. This z-score is referred to as z0.025, and sets the boundary for the rejection region. If the calculated test statistic is greater than z0.025, the null hypothesis is rejected in a right-tailed test, or if it is less than -z0.025, it is rejected in a left-tailed test.