Question

5. The Triple Blood Test screens pregnant women for the genetic disorder, Down syndrome. This syndrome occurs in about 1 in 800 live births and arises from an error in cell division that results in a fetus having an extra copy of chromosome 21. The chance of having a baby with Downsyndrome increases after a woman is 35 years old.

A study (J. Haddow et al.,New England Journal of Medicine, vol. 330, pp. 1114-1118, 1994) of5282 women aged 35 or over analyzed the Triple Blood Test to test is accuracy. It was reported that of the 5282 women, “48 of the 54 cases of Down syndrome would have been identified using the test and 25 percent of the unaffected pregnancies would have been identified as being high risk for Down syndrome (these are the false positives.)”

(a)(2 points) Construct a table that shows the counts for the possible outcomes of the blood test and whether the fetus has Down syndrome. ( Include row and column totals as well.) Use the following notation:D means Down syndrome is present,D means the fetus is unaffected. POS means that the blood test was positive, NEG means it was negative.

(b)(1 point) Assuming the sample is representative of the population, estimate the probability of a positive test for a randomly selected pregnant woman 35 years or over.

(c)(2 points) Given that that diagnostic test result is positive, estimate the probability that down syndrome truly is present.

(d)(2 points) Are the events POS and D independent or dependent? Is the answer what one should expect in this context? Explain.

Answer 1