For Large Numbers of Degrees of Freedom, the Critical $\chi ^ { 2 }$

Multiple Choice

For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows:
$$\chi ^ { 2 } = \frac { 1 } { 2 } ( \mathrm { z } + \sqrt { 2 \mathrm { k } - 1 } ) ^ { 2 }$$
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 two-tailed hypothesis test with $\mathrm { n } = 146$ and $\alpha = 0.10$ .

A) $\chi ^ { 2 } \approx 123.559$ and $\chi ^ { 2 } \approx 167.079$
B) $\chi ^ { 2 } \approx 118.791$ and $\chi ^ { 2 } \approx 174.915$
C) $\chi ^ { 2 } \approx 124.484$ and $\chi ^ { 2 } \approx 168.154$
D) $\chi ^ { 2 } \approx 117.888$ and $\chi ^ { 2 } \approx 173.818$