What Equation to use to construct a 99\% lower confidence bound for \sigma^{2}?

UkusakazaL

UkusakazaL

Answered question

2021-08-05

25.623.826.523.924.824.720.92622.227
What Equation to use to construct a 99% lower confidence bound for σ2

Answer & Explanation

Ian Adams

Ian Adams

Skilled2021-08-17Added 163 answers

Step 1
Given observation and calculation of mean and standard deviation is shown below
Data25.623.826.523.924.824.720.92622.227Sum=245.4Mean=x=245.410=24.540Variance s2=t=110(x1x)2n1=32.92101=3.66s=i=110(xix)2n1=32.92101=1.91
Step 2
99% confidence interval for the population variance is given by
CI=(n1)s2χ{α2}2σ2(n1)s2χ1α22
χ{α2}2=χ0.0122=χ0.0052=23.5894 
χ1α22=χ10.0122=χ0.9952=1.7349 
CI=(101)3.6623.5894σ2(101)3.661.7349
CI=1.3964σ218.9867
99% lower confidence bound for σ2 is
1.3964σ2

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