To determine the critical value for the chi-square test, let's follow these steps:
1. Determine the Degrees of Freedom (df):
- The degrees of freedom for this test is given as 16.
2. Choose the level of significance (alpha):
- The level of significance (alpha) chosen by the social scientist is 0.01.
3. Locate the critical value from the chi-square distribution table:
- In using the chi-square distribution table for df = 16 and alpha = 0.01, we need to find the intersection of the row corresponding to df = 16 and the column corresponding to alpha = 0.01.
From the chi-square distribution table provided:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{df} & \text{0.05} & \text{0.01} & \text{df} \\
\hline
1 & 3.84 & 6.64 & 16 \\
\hline
\end{array}
\][/tex]
The critical value for a chi-square distribution with 16 degrees of freedom and an alpha of 0.01 is 6.64.
Therefore, the critical value of chi-square for this test is 6.64.
