A sample of 200 units has a variance of 1. Find a 99% Standard Deviation Confidence Interval

Enter N	Enter Sample Variance s2	Enter Confidence Interval %

    

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A sample of 200 units has a variance σ² of 1. Find a 99% confidence interval of the standard deviation σ

Confidence Interval Formula for σ is as follows:
Square Root((n - 1)s²/χ²_α/2) < σ < Square Root((n - 1)s²/χ²_{1 - α/2}) where:
(n - 1) = Degrees of Freedom, s² = sample variance and α = 1 - Confidence Percentage

First find degrees of freedom:
Degrees of Freedom = n - 1
Degrees of Freedom = 200 - 1
Degrees of Freedom = 199

Calculate α:
α = 1 - confidence%
α = 1 - 0.99
α = 0.01

Find low end confidence interval value:
α_{low end} = α/2
α_{low end} = 0.01/2
α_{low end} = 0.005

Find low end χ² value for 0.005
χ²_0.005 = 254.135 <--- Value can be found on Excel using =CHIINV(0.005,199)

Calculate low end confidence interval total:
Low End = Square Root((n - 1)s²/χ²_α/2)
Low End = √(199)(1)/254.135)
Low End = √199/254.135
Low End = √0.78304837979814
Low End = 0.8849

Find high end confidence interval value:
α_{high end} = 1 - α/2
α_{high end} = 1 - 0.01/2
α_{high end} = 0.995

Find high end χ² value for 0.995
χ²_0.995 = 151.3697 <--- Value can be found on Excel using =CHIINV(0.995,199)

Calculate high end confidence interval total:
High End = Square Root((n - 1)s²/χ²_{1 - α/2})
High End = √(199)(1)/151.3697)
High End = √199/151.3697
High End = √1.3146620492741
High End = 1.1466

Now we have everything, display our interval answer:

You have 2 free calculationss remaining

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What this means is if we repeated experiments, the proportion of such intervals that contain σ would be 99%

Confidence Interval for Variance and Standard Deviation Calculator Video

Tags:

• confidence interval for variance and standard deviation
• confidence interval
• degrees of freedom
• standard deviation
• variance

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