A social scientist is interested in opinions about same-sex marriage. He speculates that younger people are more supportive of same-sex marriage compared to older age groups. He locates a public opinion data set including 850 people and begins his analysis to test this hypothesis. He chooses an alpha of 0.01. His results are in the chart.

Click on the correct critical value of chi-square for this test.

Critical values of chi-square:

\begin{tabular}{|c|c|c|}
\hline
df & 0.05 & 0.01 \\
\hline
1 & 3.84 & 6.64 \\
\hline
2 & 5.99 & 9.21 \\
\hline
3 & 7.82 & 11.34 \\
\hline
4 & 9.49 & 13.28 \\
\hline
5 & 11.07 & 15.09 \\
\hline
6 & 12.59 & 16.81 \\
\hline
7 & 14.07 & 18.48 \\
\hline
\end{tabular}



Answer :

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.