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 two-tailed hypothesis test with n=104 and $\alpha = 0.10$

A) X²=85.903 and X²=122.735
B) X²=81.186 and X²=128.520
C) X²=80.300 and X²=127.406
D) X²=84.992 and X²=121.646