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

question 16

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

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Definitions:

500 mL

A volume measurement often referencing the typical amount of blood pumped by the left ventricle of the heart in one minute, or the capacity of a standard drink bottle.

Tubular Load

Amount of a substance per minute that crosses the filtration membrane into Bowman’s capsule.

Afferent Arteriole

A small artery that carries blood toward the glomeruli of the kidney, playing a key role in the regulation of blood pressure.

Filtration Membrane

A selectively permeable barrier that separates substances in a mixture based on size or other characteristics, widely used in biological and chemical processes.