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In a certain country 20% are seniors, and 40% of the seniors are vitamin D deficient, and among the non-seniors, 15% are vitamin D deficient. If a person is chosen randomly, let X be the age (1=senior, 2=not senior) of the person, and let Y be the vitamin D status (1=deficient, 2=not deficient).
(a) Let pi(ij) = P(X=i;Y=j). Obtain the table for the joint probabilities(pi(ij))
(b) Find the odds for vitamin D deficiency among seniors and among non-seniors. Also, obtain the odds ratio for vitamin deficiency for seniors to non-seniors. Interpret this odds ratio.
(c) Are age and vitamin D status independent? Explain your answer.
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