Suppose because of facility limitations, a large privately owned nursing home ha

Question

Suppose because of facility limitations, a large privately owned nursing home has been turning away large numbers of patients requesting admission. Because the nursing home receives some financial assistance from public sources, they are prohibited from making the decision concerning admission on the basis of whether payment is from Medicaid or private funds. As part of a compliance study, suppose that researchers collect the following data over a two year period. Of the 88 Medicaid patients applying for admission, 24 are admitted while 64 are not. Of the 110 privately funded patients applying for admission, 62 are admitted while 48 are not. Are admission status and funding independent?

Admitted (A)

Not Admitted

Medicaid (M)

24   

64

Privately Funded

62

48

Yes, because P(M | A) = P(M

No, because P(M | A) = P(M)

Yes, because P(M | A) is not equal to P(M)

No, because P(M | A) is not equal to P(M

Admitted (A)

Not Admitted

Medicaid (M)

24   

64

Privately Funded

62

48

Explanation / Answer

Here we have to find that admission status and funding independent.

M = Medicaid Here events

A = Admitted

so, two events are to be independent.

If, P(M l A) = P(M)

P(M l A) = P( Medicaid and Admitted) / P(Admitted) = 24/ (24 + 62) = 0.279

P(M) = Total Medicaid/ Total surveyed people = (24 + 64)/ (24 + 64 + 62 + 48) = 0.44

as these are not equal so these two are not independent.

Option D is correct.

Admitted (A) Not Admitted Total Medicaid (M) 24 64 88 Privately Funded 62 48 110 Total 86 112 198

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