Solve the problem. For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows: $\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$ where k is the number of degrees of freedom and z is the critical value. To find the lower critical value, the negative z -value is used, to find the upper critical value, the positive z -value is used. Use this approximation to estimate the critical value of $\chi ^ { 2 }$ in a right-tailed hypothesis test with n=143 and $\alpha = 0.01$
A) $\chi ^ { 2 } \approx 183.411$
B) $\chi ^ { 2 } \approx 189.286$
C) $\chi ^ { 2 } \approx 188.134$
D) $\chi ^ { 2 } \approx 184.549$

Question

Solve the problem. For large numbers of degrees of freedom, the critical  $\chi ^ { 2 }$ values can be approximated as follows: $\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$ where  k  is the number of degrees of freedom and  z  is the critical value. To find the lower critical value, the negative  z -value is used, to find the upper critical value, the positive  z -value is used. Use this approximation to estimate the critical value of $\chi ^ { 2 }$  in a right-tailed hypothesis test with  n=143  and $\alpha = 0.01$
A) $\chi ^ { 2 } \approx 183.411$
B) $\chi ^ { 2 } \approx 189.286$
C) $\chi ^ { 2 } \approx 188.134$
D) $\chi ^ { 2 } \approx 184.549$

Quizplus · Accepted Answer

The correct answer is A because $\chi ^ { 2 } \approx 183.411$ is the closest to the critical value of $\chi ^ { 2 }$ in a right-tailed hypothesis test with  n=143  and $\alpha = 0.01$.

Solve the Problem χ2\chi ^ { 2 }χ2 Values Can Be Approximated as Follows

Solve the Problem $\chi ^ { 2 }$ Values Can Be Approximated as Follows