if i have x^2 = 20.303 with 9 degrees of freedom and a significance level of .05 how do i figure out the P-value and by X^2 i mean chi square

Look at a X^2 table in the back of your statistics text.

Using the definition of recovery provided in W1: Assignment 5, determine how many participants recovered at the end of posttreatment and use a chi-square analysis to compare recovery rates across the three treatments at both posttreatment and follow-up. CBT Post treatment follow up 8, 11, 4 7, 8,0 PSY 15,15,14 10,8,11 Supp 24,17,24 24,15,26

To calculate the p-value for a chi-square test with a given chi-square value and degrees of freedom, you can follow these steps:

1. Determine the chi-square value:
In this case, the given chi-square value is x^2 = 20.303.

2. Determine the degrees of freedom (df):
The degrees of freedom for your test are 9.

3. Determine the critical value (χ²_critical):
The critical value is the chi-square value at the specified significance level and degrees of freedom. Since the significance level is 0.05 and the degrees of freedom are 9, you can consult a chi-square table or use statistical software to find the critical value. The critical value will be the value of chi-square for which the area under the chi-square distribution curve to the right is 0.05. Let's assume the critical value is χ²_critical = 16.92 (just for illustration purposes).

4. Determine the p-value:
The p-value is the probability of observing a chi-square value as extreme as or more extreme than the calculated chi-square value (20.303) assuming the null hypothesis is true. To calculate the p-value, you need to compare the calculated chi-square value with the critical value.

If the calculated chi-square value (x^2) is greater than the critical value (χ²_critical), then the p-value will be less than the significance level (0.05) and therefore statistically significant. If the calculated chi-square value is less than or equal to the critical value, the p-value will be greater than the significance level, indicating no statistical significance.

In this case, since the calculated chi-square value (20.303) is greater than the critical value (16.92), the p-value associated with it will be less than 0.05.

Remember that the exact p-value calculation involves the chi-square distribution, which can be determined using statistical software or tables. The values provided above were just for illustration purposes.