A chi-square test for independence with 8 degrees of freedom results in a test statistic of 18.21. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that:
A) p-value < 0.01
B) 0.025 > p-value > 0.01
C) 0.05 > p-value > 0.025
D) 0.10 > p-value > 0.05
I picked C 0.05> p-value> 0.025
I would pick B.
Check the table again and see what you think.
To determine the p-value for a chi-square test, we need to compare the test statistic to the critical value in the chi-square table. In this case, the test statistic is 18.21, and the degrees of freedom are 8.
Looking at the chi-square table, we can see that a test statistic of 18.21 falls between the critical values for 0.025 (with 8 degrees of freedom) and 0.01 (with 8 degrees of freedom).
Since the test statistic is larger than the critical value for 0.025, but smaller than the critical value for 0.01, we can conclude that the p-value is between 0.025 and 0.01.
Therefore, the most accurate statement that can be made about the p-value for this test is: B) 0.025 > p-value > 0.01.
To determine the p-value using the chi-square table, you need to compare the test statistic (18.21) with the critical value in the table.
1. Start by finding the critical value in the chi-square table for an alpha level of your choice (typically 0.05 or 0.01). In this case, we can assume an alpha level of 0.05.
2. Look for the row corresponding to the number of degrees of freedom (8 in this case) in the chi-square table.
3. Find the column that gives the critical value for the chosen alpha level (0.05 in this case).
4. Check if the test statistic (18.21) is greater than the critical value. If it is, then the p-value will be less than the chosen alpha level.
Based on your response, you chose option C) 0.05 > p-value > 0.025. Let's see if this is the correct answer by applying the steps above:
1. Looking at the chi-square table, for 8 degrees of freedom, the critical value at the alpha level of 0.05 is between 15.51 and 20.09.
2. Since the test statistic (18.21) is greater than 15.51, but less than 20.09, it suggests that the p-value is greater than 0.025 but less than 0.05.
Therefore, your answer appears to be correct. Option C) 0.05 > p-value > 0.025 is the most accurate statement about the p-value for this test.