Alright, let’s solve the given problem step-by-step in detail.
You are given the expression for [tex]\( C \)[/tex]:
[tex]\[ C = \sqrt{\frac{\chi^2}{N + \chi^2}} \][/tex]
The given values are:
[tex]\[ \chi^2 = 29,881 \][/tex]
[tex]\[ N = 282 \][/tex]
Now, let's compute the fraction inside the square root step-by-step:
1. Sum the denominator:
[tex]\[ N + \chi^2 = 282 + 29,881 = 30,163 \][/tex]
2. Form the fraction:
[tex]\[ \frac{\chi^2}{N + \chi^2} = \frac{29,881}{30,163} \][/tex]
3. Simplify the fraction numerically:
[tex]\[ \frac{29,881}{30,163} \approx 0.9906507973344827 \][/tex]
4. Compute the square root:
[tex]\[ C = \sqrt{0.9906507973344827} \][/tex]
5. Final value of [tex]\( C \)[/tex]:
[tex]\[ C \approx 0.9953144213435685 \][/tex]
Thus, the fraction [tex]\(\frac{\chi^2}{N + \chi^2}\)[/tex] simplifies to approximately 0.9906507973344827, and the value of [tex]\( C \)[/tex] is approximately 0.9953144213435685.
