11.48 Down syndrome diagnostic test The table shown, from Example 8 in Chapter 5, cross-tabulates whether a fetus has Down syndrome by whether the triple blood diagnostic test for Down syndrome is positive (that is, indicates that the fetus has Down syndrome).

a. Tabulate the conditional distributions for the blood test result, given the true Down syndrome status.

b. For the Down cases, what percentage was diagnosed as positive by the diagnostic test? For the unaffected cases, what percentage got a negative test result?

Does the diagnostic test appear to be a good one?

c. Construct the conditional distribution on Down syndrome status for those who have a positive test result.

(Hint: You condition on the first column total and find proportions in that column.) Of those cases, what percentage truly have Down syndrome? Is the result surprising? Explain why this probability is small.

Blood Test Result Down Syndrome Status Positive Negative Total D (Down) 48 6 54 D (unaffected) 1307 3921 5228 Total 1355 3927 5282