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

question 182

Multiple Choice

Solve the problem. For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows: $x ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$ , 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) \(\chi ^ { 2 } \approx 80.300\) and \(\chi ^ { 2 } \approx 127.406\)
• B) \(\chi ^ { 2 } \approx 84.992\) and \(\chi ^ { 2 } \approx 121.646\)
• C) \(\chi ^ { 2 } \approx 85.903\) and \(\chi ^ { 2 } \approx 122.735\)
• D) \(\chi ^ { 2 } \approx 81.186\) and \(\chi ^ { 2 } \approx 128.520\)

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Definitions:

François Magendie

A French physiologist known for his pioneering research in experimental physiology and his contributions to the understanding of the nervous system's functions.

Segregation

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Autonomic Nervous System (ANS)

A component of the peripheral nervous system that controls bodily functions not consciously directed, such as breathing, the heartbeat, and digestive processes.

Illness

A condition of poor health perceived or experienced by an individual as an invasion, disorder, or loss of function in one's body or mind.