Calculate confidence interval when only given alpha?Is there a formula to properly calculate the confidence interval when you're only given alpha and sample data?

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Calculate confidence interval when only given alpha?Is there a formula to properly calculate the confidence interval when you&#039;re only given alpha and sample data?

Kasen Alexander · Accepted Answer

In order to correctly construct confidence interval, first of all, you need a &quot;pivot&quot; T such that1. T is a function of all data X1,X2,…,Xn.2. T is a function of μThe distribution of T is know, and it is not a function of μFor example, T=x―−μσn is a pivot, and T∼N(0,1) regardless of the value of μ (if the sample size is large enough, say &amp;gt;30).In this case, P(a≤T≤b)=1−α, where a=−Zα2 and b=Zα2. So the &quot;natural&quot; confidence interval is (x―−Zα2(σn),x―+Zα2(σn)), where Zα2 is such that P(z&amp;gt;Zα2)=α2.Zα2 can be calculated using the R command q‖1−α2‖This is just an example when we know the pivot has the normal distribution. There exist other cases where the pivot we constructed doesn&#039;t have a normal distribution, and the calculation in that case would be a little bit different than this. I don&#039;t think there exists a formula that can be applied to any situation.

Calculate confidence interval when only given alpha? Is there

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