In the DOS, we are interested in testing the following hypothesis concerning the distribution of depression diagnosis for the entire sample:

\[\begin{aligned}\operatorname{Pr}(\text { No depression }) & =0.5 \\\operatorname{Pr}(\text { Minor depression }) & =0.3 \\\operatorname{Pr}(\text { Major depression }) & =0.2\end{aligned}\]

(a) Use the DOS data to test this hypothesis. First, use the chi-square test and then follow with the exact test.

(b) Compare the results from the chi-square and exact test.

(c) Describe your findings and conclusions based on the test results.