A sample of 30 units has a variance of 1.21. Find a 95% Variance Confidence Interval

Enter N	Enter Sample Variance s2	Enter Confidence Interval %

    

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A sample of 30 units has a variance σ² of 1.21. Find a 95% confidence interval of the variance σ²

Confidence Interval Formula for σ² is as follows:
(n - 1)s²/χ²_α/2 < σ² < (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 = 30 - 1
Degrees of Freedom = 29

Calculate α:
α = 1 - confidence%
α = 1 - 0.95
α = 0.05

Find low end confidence interval value:
α_{low end} = α/2
α_{low end} = 0.05/2
α_{low end} = 0.025

Find low end χ² value for 0.025
χ²_0.025 = 45.7223 <--- Value can be found on Excel using =CHIINV(0.025,29)

Calculate low end confidence interval total:
Low End = (n - 1)s²/χ²_α/2
Low End = (29)(1.21)/45.7223
Low End = 35.09/45.7223
Low End = 0.7675

Find high end confidence interval value:
α_{high end} = 1 - α/2
α_{high end} = 1 - 0.05/2
α_{high end} = 0.975

Find high end χ² value for 0.975
χ²_0.975 = 16.0471 <--- Value can be found on Excel using =CHIINV(0.975,29)

Calculate high end confidence interval total:
High End = (n - 1)s²/χ²_{1 - α/2}
High End = (29)(1.21)/16.0471
High End = 35.09/16.0471
High End = 2.1867

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 σ² would be 95%

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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