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 $\chi ^ { 2 }$ in a two-tailed hypothesis test with n=104 and $\alpha = 0.10$

A) $\chi ^ { 2 } \approx 84.992 \text { and } \chi ^ { 2 } \approx 121.646$
B) $\chi ^ { 2 } \approx 81.186 \text { and } \chi ^ { 2 } \approx 128.520$
C) $\chi ^ { 2 } \approx 80.300 \text { and } \chi ^ { 2 } \approx 127.406$
D) $\chi ^ { 2 } \approx 85.903 \text { and } \chi ^ { 2 } \approx 122.735$