Find the critical values, $\mathrm { X } _ { \mathrm { R } } ^ { 2 } \text { and } \mathrm { X } _ { \mathrm { L } } ^ { 2 }$ , for c = 0.95 and 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

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The critical values $\mathrm { X } _ { \mathrm { R } } ^ { 2 }$ and $\mathrm { X } _ { \mathrm { L } } ^ { 2 }$ for a chi-square distribution with $n - 1$ degrees of freedom (where $n$ is the sample size) and a confidence level $c$ can be found using chi-square distribution tables or software. For $c = 0.95$ and $n = 12$, the degrees of freedom is $11$. The critical values corresponding to the lower and upper tails for a 95% confidence interval (or 0.025 in each tail of a two-tailed distribution) are approximately 3.816 and 21.920, respectively.

Find the Critical Values XR2 and XL2\mathrm { X } _ { \mathrm { R } } ^ { 2 } \text { and } \mathrm { X } _ { \mathrm { L } } ^ { 2 }XR2​ and XL2​

Find the Critical Values $\mathrm { X } _ { \mathrm { R } } ^ { 2 } \text { and } \mathrm { X } _ { \mathrm { L } } ^ { 2 }$