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

Multiple Choice

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 $x ^ { 2 }$ in a right-tailed hypothesis test with n=143 and $\alpha = 0.01$

A) $\chi ^ { 2 } = 183.411$
B) $\chi ^ { 2 } = 189.286$
C) $\chi ^ { 2 } = 188.134$
D) $\chi ^ { 2 } = 184.549$