The term \( z_{\alpha/2} \) is known as the critical value from the standard normal distribution (Z-distribution) that corresponds to a specified significance level \(\alpha\). It is used in statistical hypothesis testing, particularly in the context of constructing confidence intervals.
In a two-tailed test, \( z_{\alpha/2} \) represents the value such that the area under the standard normal curve beyond that value in both tails sums to \(\alpha\). For example, if you were constructing a 95% confidence interval, \( \alpha = 0.05 \), and thus \( z_{\alpha/2} \) would correspond to \( z_{0.025} \), which is approximately 1.96.
In summary, \( z_{\alpha/2} \) is used to determine the boundaries of confidence intervals or test statistics in hypothesis testing.
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