In a study of the relationship between health risk and incom

In a study of the relationship between health risk and income, a large group of people living in Massachusetts were asked a series of questions. Some of the results are shown in the following table. Here stressed means that the person reported that most days are extremely stressful or quite stressful; not stressed means that the person reported that most days are a bit stressful, not very stressful, or not at all stressful. (a) What is the probability that someone in this study is stressed? (b) Given that someone in this study is from the high income group, what is the probability that the person is stressed? (c) Is being stressed independent of having high income? Why or why not?

Solution

a)

P(Str) = N(Str) / N(tot) = 1015/6549

= 0.154985494

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b)

P(Str|High) = N(Str and High)/N(high)

= 216/2115

= 0.10212766 [answer]

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c)

No. As you can see, the overall probability that a person is stressed (part a) is not equal to the probability of being stressed in high income (part b).

Thus, they are not independent.