if critical value is 9.35 the degree of freedom is 3 what is the significant level

To find the significance level (\(\alpha\)) corresponding to a given critical value and degree of freedom, we typically refer to a chi-square distribution table (for chi-square tests). In this case, you're asking for the significance level with:

- Critical value (\(\chi^2\)): 9.35
- Degrees of freedom (df): 3

Let’s find the significance level:

1. A \(\chi^2\) critical value of 9.35 with 3 degrees of freedom corresponds to a significance level \(\alpha\) of approximately **0.025** (or 2.5%).

This means that if the calculated chi-square statistic exceeds 9.35 with 3 degrees of freedom, the result would be statistically significant at the 2.5% level.

### Do you need more details or have any questions about this?

Here are 5 related questions:
1. How does the chi-square distribution change with degrees of freedom?
2. What is the difference between one-tailed and two-tailed significance tests?
3. How can the critical value be used in hypothesis testing?
4. What are the common significance levels used in statistics (e.g., 0.05, 0.01)?
5. How do we compute p-values from chi-square test results?

**Tip:** The smaller the significance level (\(\alpha\)), the stronger the evidence must be against the null hypothesis to reject it.

Learn how to determine the significance level for a chi-square test when the critical value is 9.35 and the degrees of freedom are 3. This example demonstrates how to use the chi-square distribution and critical value table lookup, suitable for undergraduate statistics and probability students.

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