In a study to examine whether the income level has anything

In a study to examine whether the income level has anything to do with the stress level a random sample of 6,549 persons is selected. These data is presented as shown below. What is the probability that someone in this study is stressed? Given that someone in the study is from the high income group, what is the probability that the person is stressed? Compare your answers to parts and Is being stressed is independent of having high income? Why or why not?

Solution

a)

P(stressed) = n(stressed)/N = 1016/6549 = 0.155138189

b)

P(stressed|high income) = n(stressed and high)/n(high) = 216/2115 = 0.10212766 [answer]

c)

NO. If they were independent, then P(stressed) = P(stressed|high). Thus, THEY ARE NOT INDPEPENDENT.