Confidence Itervals; Zα and Zα2I'm confused about what exactly Zα is, does there exist a formula for it in terms of α? IF so, is there also one for Zα2?

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Confidence Itervals; Zα and Zα2I&#039;m confused about what exactly Zα is, does there exist a formula for it in terms of α? IF so, is there also one for Zα2?

Rachettolyf8 · Accepted Answer

Commonly, zβ refers to the point (number) such that Pr(Z&amp;gt;zβ)=β. Here Z is the standard normal distribution. So for instance zβ, where β=0.005, refers to the point z such that Pr(Z&amp;gt;z)=0.005. It turns out that in this case zβ≈2.57. So the probability that a random variable with standard normal distribution is bigger than 2.57 is 0.005. Thus the area under the standard normal curve in the right tail past 2.57 is 0.005.This kind of information is needed when we calculate confidence intervals when the normal distibution provides a reasonable fit, and also in hypothesis testing in similar situations.There is no nice formula for zβ in terms of β. But many pieces of software, including standard spreadsheets, will compute it for you. There are also online calculators that will do it.Before the computers everywhere era, people used tables of the standard normal to locate zβ for the β they were interested in, typically numbers like β=0.05,0.025, or 0.01, and so on.Anyone who has done statistics probably remembers forever that z0.025≈1.96.

Confidence Itervals; \(\displaystyle{Z}_{{\alpha}}\ \text{and}\ {Z}_{{\frac{\alpha}{{2}}}}\) I'm confused about

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