Variance of a fill volume
Twenty-seven bottles of juice have sample standard deviation 5.86 ml. Give a 95% confidence interval for the variance \sigma^2. Use \chi^2_{26,\,0.975}=41.92 and \chi^2_{26,\,0.025}=13.84.
Worked answer (click to show)
(n-1)s^2=26\times 5.86^2=893.0. The interval is
\left(\frac{893.0}{41.92},\,\frac{893.0}{13.84}\right)=(21.3,\,64.5).