$$\text { Find the critical values, } \chi _ { 1 } ^ { 2 } - \alpha / 2 \text { and } \chi _ { \alpha / 2 } ^ { 2 } \text {, for } 95 \% \text { confidence and } \mathrm { n } = 12$$
A) 3.816 and 21.920
B) 3.053 and 24.725
C) 4.575 and 26.757
D) 2.603 and 19.675

Question

Quizplus · Accepted Answer

For a 95% confidence interval and $n = 12$, the degrees of freedom ($df$) for the chi-square distribution is $n - 1 = 11$. The critical values $\chi_{1-\alpha/2}^2$ and $\chi_{\alpha/2}^2$ correspond to the upper and lower tails of the chi-square distribution for 95% confidence. Looking up these values in a chi-square distribution table or using a calculator for $df = 11$, the critical values are approximately 3.816 and 21.920, respectively.

A) 3816 and 21