Find the critical value and rejection region for the type of chi-square test with sample size n and level of significance α $\alpha$ Two-tailed test, $\mathrm { n } = 12 \cdot \alpha = 0.05$ A) $\chi ^ { 2 } \mathrm {~L} = 3.816 , \chi ^ { 2 } \mathrm { R } = 21.920 ; \chi ^ { 2 } 21.920$ B) $\chi ^ { 2 } \mathrm {~L} = 2.603 , \chi ^ { 2 } \mathrm { R } = 26.757 ; \chi ^ { 2 } 26.757$ C) $\chi ^ { 2 } \mathrm {~L} = 3.053 , \chi ^ { 2 } \mathrm { R } = 24.725 ; \chi ^ { 2 } 24.725$ D) $\chi ^ { 2 } \mathrm {~L} = 4.575 , \chi ^ { 2 } \mathrm { R } = 19.675 ; \chi ^ { 2 } 19.675$

Question

Find the critical value and rejection region for the type of chi-square test with sample size n and level of significance α $\alpha$ Two-tailed test, $\mathrm { n } = 12 \cdot \alpha = 0.05$ A) $\chi ^ { 2 } \mathrm {~L} = 3.816 , \chi ^ { 2 } \mathrm { R } = 21.920 ; \chi ^ { 2 } < 3.816 , \chi ^ { 2 } > 21.920$ B) $\chi ^ { 2 } \mathrm {~L} = 2.603 , \chi ^ { 2 } \mathrm { R } = 26.757 ; \chi ^ { 2 } < 2.603 , \chi ^ { 2 } > 26.757$ C) $\chi ^ { 2 } \mathrm {~L} = 3.053 , \chi ^ { 2 } \mathrm { R } = 24.725 ; \chi ^ { 2 } < 3.053 , \chi ^ { 2 } > 24.725$ D) $\chi ^ { 2 } \mathrm {~L} = 4.575 , \chi ^ { 2 } \mathrm { R } = 19.675 ; \chi ^ { 2 } < 4.575 , \chi ^ { 2 } > 19.675$

Quizplus · Accepted Answer

For a two-tailed chi-square test with $n = 12$ and $\alpha = 0.05$, the degrees of freedom ($df$) is $n - 1 = 11$. The critical values for $\alpha/2 = 0.025$ in each tail from chi-square distribution tables are $\chi^2_L = 3.816$ and $\chi^2_R = 21.920$, making option A correct.

Find the Critical Value and Rejection Region for the Type α\alphaα

Find the Critical Value and Rejection Region for the Type $\alpha$