Answer:
Correct option: (b) 32.357 and 71.420
Explanation:
The confidence interval for population variance σ² is:
[tex]\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1) }}\leq \sigma^{2}\leq \frac{(n-1)s^{2}}{\chi^{2}_{(1-\alpha/2), (n-1) }}[/tex]
Given:
[tex]n=51\\\alpha =1-0.95=0.05[/tex]
Compute the critical values of chi-square as follows:
[tex]\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.025,50}=71.42[/tex]
[tex]\chi^{2}_{(1-\alpha/2), (n-1)}=\chi^{2}_{0.975,50}=32.36[/tex]
Use the chi-square table for the critical value.
Thus, the critical values are 32.36 and 71.42.
