Find the rejection region for a one-dimensional chi-square test of a null hypothesis concerning $p _ { 1 } , p _ { 2 } , \ldots p _ { \mathrm { k } }$ if $k = 4$ and $\alpha = .01$.
A) $\chi ^ { 2 } 11.345$
B) $\chi ^ { 2 } 0.115$
C) $\chi ^ { 2 } 13.277$
D) $\chi ^ { 2 } 15.086$

Question

Find the rejection region for a one-dimensional chi-square test of a null hypothesis concerning $p _ { 1 } , p _ { 2 } , \ldots p _ { \mathrm { k } }$ if $k = 4$ and $\alpha = .01$.
A) $\chi ^ { 2 } > 11.345$
B) $\chi ^ { 2 } > 0.115$
C) $\chi ^ { 2 } > 13.277$
D) $\chi ^ { 2 } > 15.086$

Quizplus · Accepted Answer

For a chi-square test with $k = 4$ categories, the degrees of freedom ($df$) are $k - 1 = 3$. Looking up the critical value for $\alpha = .01$ in a chi-square distribution table for $3$ degrees of freedom, the correct rejection region is $\chi ^ { 2 } > 11.345$.

Find the Rejection Region for a One-Dimensional Chi-Square Test of a Null