Sample Size,  n=  12
Sample Standard Deviation,  s = √(Σ(X- x̅ )²/(n-1) ) =
417.5571
Confidence Level,  CL=  0.80
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Degrees of Freedom,  DF=n-1 =   11
alpha,  α=1-CL=  0.2
alpha/2 ,  α/2=  0.1
Lower Chi-Square Value=  χ²1-α/2 = Â
5.5778
Upper Chi-Square Value=  χ²α/2 = Â
17.2750
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confidence interval for variance is Â
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lower bound=  (n-1)s²/χ²α/2 = Â
111021.24
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upper bound=  (n-1)s²/χ²1-α/2 = Â
343844.91
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confidence interval for population std dev is
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lower bound=  √(lower bound
variance)=Â Â 333.2
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upper bound=  √(upper bound of
variance=Â Â 586.4
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