Question

To construct a 96% confidence interval for variance we took a sample of 20 objects. The lower and upper critical values are___and___ , respectively.

Answer 1

$100(1-\alpha)% = 96% \Rightarrow \alpha = 0.04$$100(1-\alpha) = 96 \Rightarrow \alpha = 0.04$

$n=20$

$\chi^{2}_{n-1, 1-\frac{\alpha}{2}} = \chi^{2}_{19,0.98} = 8.56703542$

$\chi^{2}_{n-1, \frac{\alpha}{2}} = \chi^{2}_{19,0.02} = 33.68742507$

Thus, the critical values are 8.567035 and 33.687425 respectively.