Assume That a Hypothesis Test of the Given Claim Will $\chi ^ { 2 }$

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
-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 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 right-tailed hypothesis test with $\mathrm { n } = 146$ and $\alpha = 0.01$

A) $\chi ^ { 2 } \approx 192.742$
B) $\chi ^ { 2 } \approx 186.824$
C) $\chi ^ { 2 } \approx 187.961$
D) $\chi ^ { 2 } \approx 191.590$