To solve $P(\chi^2_{11} > 6.098)$, we again need to use the chi-square distribution, where:

• Degrees of freedom ($df$) = 11
• The chi-square value is 6.098.

We will compute $P(\chi^2 > 6.098)$ by calculating the complement of the cumulative distribution function (CDF).

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In the meantime, you could look up or use a statistical calculator to compute $P(\chi^2_{11} > 6.098)$. Let me know if you'd like to explore this further or have any questions.

Here are some related questions to consider:

1. How do cumulative distribution functions work in chi-square distributions?
2. How can you compute chi-square probabilities using tables?
3. What is the significance of the degrees of freedom in hypothesis testing?
4. Can chi-square tests be used for small sample sizes?
5. How is chi-square distribution different from normal distribution?

Tip: When computing probabilities for chi-square distributions, it's often helpful to use software tools or statistical tables, as chi-square distributions are skewed, especially for small degrees of freedom.