What is 𝑧𝛼/ 2 in stistics
In statistics, 𝑧𝛼/2 refers to the critical value of the standard normal distribution at significance level α/2.
The standard normal distribution, also known as the Z-distribution, is a bell-shaped distribution with a mean of 0 and a standard deviation of 1. It is often used in hypothesis testing and confidence intervals.
The critical value 𝑧𝛼/2 is used to determine the rejection region in hypothesis testing or the boundaries for a confidence interval. It corresponds to the specific α/2 probability in the tails of the standard normal distribution.
For example, if α = 0.05 (significance level of 5%), 𝑧0.025/2 would refer to the critical value where the area under the curve in the left tail is 0.025 and the area in the right tail is also 0.025. This critical value is approximately 1.96.
Using 𝑧𝛼/2, statisticians can determine the appropriate cutoff point for making decisions in hypothesis testing or calculate confidence intervals based on the standard normal distribution.