Find low end confidence interval value: αlow end = α/2 αlow end = 0.01/2 αlow end = 0.005
Find low end χ2 value for 0.005 χ20.005 = 32.8015 <--- Value can be found on Excel using =CHIINV(0.005,15)
Calculate low end confidence interval total: Low End = (n - 1)s2/χ2α/2 Low End = (15)(4.84)/32.8015 Low End = 72.6/32.8015 Low End = 2.2133
Find high end confidence interval value: αhigh end = 1 - α/2 αhigh end = 1 - 0.01/2 αhigh end = 0.995
Find high end χ2 value for 0.995 χ20.995 = 4.6009 <--- Value can be found on Excel using =CHIINV(0.995,15)
Calculate high end confidence interval total: High End = (n - 1)s2/χ21 - α/2 High End = (15)(4.84)/4.6009 High End = 72.6/4.6009 High End = 15.7795
Now we have everything, display our interval answer:
2.2133 < σ2 < 15.7795 <---- This is our 99% confidence interval
You have 2 free calculationss remaining
What this means is if we repeated experiments, the proportion of such intervals that contain σ2 would be 99%
What is the Answer?
2.2133 < σ2 < 15.7795 <---- This is our 99% confidence interval
How does the Confidence Interval for Variance and Standard Deviation Calculator work?
Free Confidence Interval for Variance and Standard Deviation Calculator - Calculates a (95% - 99%) estimation of confidence interval for the standard deviation or variance using the χ2 method with (n - 1) degrees of freedom. This calculator has 3 inputs.
What 4 formulas are used for the Confidence Interval for Variance and Standard Deviation Calculator?