Find Critical Values for the Chi-Square Distribution
-Find the critical values, $\chi _ { 1 } ^ { 2 } - \alpha / 2$ and $\chi _ { \alpha / 2 } ^ { 2 }$, for $95 \%$ 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 level and $n = 12$, the degrees of freedom ($df$) is $n - 1 = 11$. The critical values for $\chi^2$ with $df = 11$ at the 95% confidence level are approximately $3.816$ for the lower tail ($\chi_{0.025}^2$) and $21.920$ for the upper tail ($\chi_{0.975}^2$), matching option A.

Find Critical Values for the Chi-Square Distribution -Find the Critical χ12−α/2\chi _ { 1 } ^ { 2 } - \alpha / 2χ12​−α/2

Find Critical Values for the Chi-Square Distribution
-Find the Critical $\chi _ { 1 } ^ { 2 } - \alpha / 2$