How do you calculate the critical value of X^2 at the 5% level of significance in a chi squared? And how do you calculate the degree of freedom?
The textbook wording makes no sense and doesn't show it fully and I've read it over at least 10 times now to try to figure out how they get it.
Thanks for the help!
To calculate the critical value of X^2 at the 5% level of significance in a chi-squared distribution, you need to follow a few steps.
1. Determine the degrees of freedom (df): The degree of freedom is based on the number of categories or groups involved in the data. For a chi-squared test, it is calculated as df = (number of categories) - 1.
2. Use a chi-squared distribution table: With the degrees of freedom in mind, refer to a chi-squared distribution table (also known as the chi-squared critical values table). You can find these tables in statistics textbooks, online resources, or statistical software packages.
3. Locate the 5% level of significance: Scan the table to find the row that corresponds to the degrees of freedom you calculated in step 1. Then, identify the column that corresponds to the desired level of significance (in this case, 5%).
4. Find the critical value: Going to the intersection of the row and column you found in step 3, you will find a value denoted as the critical value. This value represents the threshold that your chi-squared test statistic must exceed for the test to be statistically significant at the specified level of significance.
Please note that the values in the chi-squared table are often rounded off. If you need a more precise critical value, you can use statistical software or online calculators that directly provide the critical value for a given level of significance and degrees of freedom.
Remember, the critical value determines the rejection region in hypothesis testing. If your test statistic exceeds the critical value, you can reject the null hypothesis in favor of the alternative hypothesis.