Question

1. The results of a survey are presented in the following contingency table.

	Go to the gym regularly	Don’t go to the gym regularly
See a doctor regularly	150	280
Don’t see a doctor regularly	200	100

1. Convert the contingency table into a joint probability table. (5pts)

2. Is seeing a doctor regularly independent of whether or not a person goes to the gym regularly? (Test independence). Show your work. (10pts)

Answer 1

	Go to the gym regularly	Don’t go to the gym regularly
See a doctor regularly	150	280
Don’t see a doctor regularly	200	100

joint probability table is

	Go to the gym regularly	Don’t go to the gym regularly
See a doctor regularly	150/730=0.2055	280/730=0.3836
Don’t see a doctor regularly	200/730=0.2740	100/730=0.1370

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P(go to gym regular) = 0.2055 + 0.2740=0.4795

P(see a doctor regular) = 0.2055 + 0.3836 = 0.5890

P(go to gym regular and see doctor regular) = 0.2055

P(go to gym regular) * P(see a doctor regular) = 0.4795 * 0.5890 = 0.2824

since, P(go to gym regular) * P(see a doctor regular) ╪ P(go to gym regular and see doctor regular)

So, seeing a doctor regularly is not independent of whether a person goes to the gym regularly