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 $\mathrm { k }$ is the number of degrees of freedom and $\mathrm { z }$ is the critical value. To find the lower critical value, the negat 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 $\mathrm { n } = 144$ and $\alpha = 0.10$ .

A) $\chi ^ { 2 } \approx 116.985$ and $\chi ^ { 2 } \approx 172.721$
B) $\chi ^ { 2 } \approx 116.082$ and $\chi ^ { 2 } \approx 171.624$
C) $\chi ^ { 2 } \approx 122.635$ and $\chi ^ { 2 } \approx 166.004$
D) $\chi ^ { 2 } \approx 121.710$ and $\chi ^ { 2 } \approx 164.928$