Find the Critical Value or Values Of $\chi ^ { 2 }$

Multiple Choice

Find the critical value or values of $\chi ^ { 2 }$ based on the given information.
-For large numbers of degrees of freedom, the critical $x ^ { 2 }$ values can be approximated as follows: $\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$ where $\mathrm { k }$ is the number of degrees of freedom and $\mathrm { z }$ 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) $\chi ^ { 2 } \approx 189.286$
B) $\chi ^ { 2 } \approx 188.134$
C) $X ^ { 2 } \approx 184.549$
D) $\chi ^ { 2 } \approx 183.411$