Confidence Interval for Proportion 1 population

Confidence Interval for the Standard Deviation σ

The χ² distribution is not symmetric and there is a different distribution for each sample size. Thus there are two critical values for the confidence interval.

Left and right critical values
of chi squared χ²_L and χ²_R

For right, left or two tailed hypothesis tests, critical values of χ² can be found in Table A-4. First compute (α ÷ 2) and 1.000 – (α ÷ 2). Look for the same area values in the column titles and look in the row for the number of degrees of freedom. df = n - 1
Because the χ² distribution is asymmetric the right critical value is not equal to the left critical value as they are in the z and t distributions.

Confidence Interval

Because the χ² distribution is asymmetric the limits of the confidence interval are computed directly without computing the margin of error.