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

question 38

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 \(\chi ^ { 2 } \approx 173.818\)

---

Definitions:

Nation States

Political entities consisting of a clearly defined territory and population that is politically organized under a sovereign government.

International Organizations

Entities established by treaties between governments for purposes of conducting activities and fostering cooperation among member countries across borders.

International Agreements

Formal arrangements between two or more countries governed by international law, which can relate to trade, peace, cooperation, or other mutual interests.

Neoliberal Globalization

Refers to the process of accelerating economic integration, market deregulation, and diminishing state intervention across countries, pushed by neoliberal policies.