Question

1. A study was conducted to better understand the relationship between income level and obesity in a county in Texas. Participants in the study were grouped into three income categories: high (top quartile), medium (middle two quartiles), and low (bottom quartile). The study also used their BMI to determine whether or not they were obese.

The results show that 37% of the low-income group, 31% of the medium-income group, and 20% of the high-income group were obese.

a. Draw a probability tree for this scenario. Label the outcomes and indicate the appropriate probabilities on all branches of the tree.

b. What proportion of these participants were obese and in the medium-income group?

c. What proportion of these participants were not obese?

Answer 1

Question (a)

The tree diagram with outcomes appropriate probabilities on all branches of the tree including the final probabilities is as follows

Question (b)

Proportion of these participants were obese and in the medium-income group = 0.10323

Question (c)

Proportion of these participants were not obese = 0.20979 + 0.22977 + 0.2664

= 0.70596