Solve the Problem $\chi ^ { 2 }$ Values Can Be Approximated as Follows

question 21

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 $\chi ^ { 2 }$ in a two-tailed hypothesis test with n=104 and $\alpha = 0.10$

• A) \(\chi ^ { 2 } \approx 84.992 \text { and } \chi ^ { 2 } \approx 121.646\)
• B) \(\chi ^ { 2 } \approx 81.186 \text { and } \chi ^ { 2 } \approx 128.520\)
• C) \(\chi ^ { 2 } \approx 80.300 \text { and } \chi ^ { 2 } \approx 127.406\)
• D) \(\chi ^ { 2 } \approx 85.903 \text { and } \chi ^ { 2 } \approx 122.735\)

---

Definitions:

Preventative Facework

Strategies employed proactively to maintain or protect an individual's self-image or reputation in social interactions.

Facework

Strategies used to manage one's own image or face in social interactions, and to uphold or repair the face of others.

Face

is a sociolinguistic concept that refers to an individual's projected image or social value within interpersonal communications.

Self-worth

The subjective evaluation of one's own value as a person, often influenced by self-perception and external validation.