A clarification on the level of confidence for a Chi-squared distribution Suppose we have \ch

Kelvin Gregory

Kelvin Gregory

Answered question

2022-03-02

A clarification on the level of confidence for a Chi-squared distribution
Suppose we have χ1α,292=45.22, where the Chi-squared distribution has 29 degrees of freedom and (1α)% level of confidence. How then do we compute 1α? The notation of χ2. I've found in books and online sources all come in the form of χc2, where c is the degrees of freedom.
I know this question seems trivial, but I'm still relatively new to Statistics.. Some clarification will be great!

Answer & Explanation

ofisu2n3

ofisu2n3

Beginner2022-03-03Added 4 answers

Recall that for XChiSquare(ν), that is to say χν2, we have
fX(x)=xν21ex22ν2Γ(ν2),x>0,
hence, Pr[Xχ1α,ν2]=1α.
In other words, χ1α,ν2 is the 1α quantile of the chi-square distribution with ν degrees of freedom. Given this value and ν, the computation for α involves computing an integral; in your case, numeric evaluation of x=045.22fX(x),dx0.971992,
or a0.028.

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