Questions: 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 relative risk of being depressed for those who wear cotton clothes? Round your answer to two decimal places. Depressed Not depressed Total ------------------------------------------- Cotton 122 189 311 Not cotton 420 263 683 Total 542 452 994 Provide your answer below:

Solution Steps

The data from the survey is organized in a contingency table as follows:

\[ \begin{array}{|l|c|c|c|} \hline & \text{Depressed} & \text{Not depressed} & \text{Total} \\ \hline \text{Cotton} & 122 & 189 & 311 \\ \hline \text{Not cotton} & 420 & 263 & 683 \\ \hline \text{Total} & 542 & 452 & 994 \\ \hline \end{array} \]

We need to calculate the probabilities of being depressed for those who wear cotton clothes and those who do not.

1. For those who wear cotton: \[ p_1 = \frac{a}{a + b} = \frac{122}{122 + 189} = \frac{122}{311} \approx 0.3923 \]

2. For those who do not wear cotton: \[ p_2 = \frac{c}{c + d} = \frac{420}{420 + 263} = \frac{420}{683} \approx 0.6149 \]

The relative risk (RR) is calculated using the formula: \[ RR = \frac{p_1}{p_2} = \frac{0.3923}{0.6149} \approx 0.6397 \]

Rounding the relative risk to two decimal places gives: \[ RR \approx 0.64 \]

Final Answer