Question Researchers wanted to study if wearing cotton clothes is related to depression. They surveyed a large group of people. The data are shown in the contingency table below. What is the odds ratio for depressed people wearing cotton clothes against people who don't have depression wearing cotton clothes? Round your answer to two decimal places. \begin{tabular}{|l|c|c|c|} \hline & Depressed & Not depressed & Total \\ \hline Cotton & 122 & 189 & 311 \\ \hline Not cotton & 420 & 263 & 683 \\ \hline Total & 542 & 452 & 994 \\ \hline \end{tabular} Provide your answer below:

Step 1 ：Given the data from the contingency table, we are asked to find the odds ratio for depressed people wearing cotton clothes against people who don't have depression wearing cotton clothes.

Step 2 ：The odds ratio is a measure of association between an exposure and an outcome. In this case, the exposure is wearing cotton clothes and the outcome is depression.

Step 3 ：The odds ratio is calculated as the odds of the outcome in the exposed group divided by the odds of the outcome in the non-exposed group.

Step 4 ：In this case, the odds of depression in the cotton group is \(\frac{122}{189}\) and the odds of depression in the non-cotton group is \(\frac{420}{263}\).

Step 5 ：The odds ratio is therefore \(\frac{\frac{122}{189}}{\frac{420}{263}}\).

Step 6 ：Calculating this gives us an odds ratio of approximately 0.4042076089695137.

Step 7 ：Final Answer: The odds ratio for depressed people wearing cotton clothes against people who don't have depression wearing cotton clothes is \(\boxed{0.40}\).