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

question 8

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

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Definitions:

Orexin

A type of neuropeptide that plays an important role in regulating arousal, wakefulness, and appetite.

Set Point

A theory suggesting that individuals have a pre-set, natural body weight or condition that the body regulates and tends to maintain.

Physical Activity

Any bodily movement produced by skeletal muscles that requires energy expenditure, including activities undertaken while working, playing, carrying out household chores, traveling, and engaging in recreational pursuits.

Stable Body Weight

A condition where an individual's body weight remains relatively constant over time, indicating a balance between calorie intake and energy expenditure.