Question

A Pap Smear is a screening procedure used to detect cervical cancer. The Center for Disease Control reports that about 8 women in 100,000 have this disease. That is, P(Cervical Cancer) = 0.00008. For women with cervical cancer, the chance of a false negative Pap Smear test result is 0.16. For women without cervical cancer, the chance of a false positive Pap Smear test result is 0.19. Use a tree diagram to model this example. Note: In the diagram you create, the first set of branches are for ‘Cervical Cancer’ and ’not Cervical Cancer'. The 2nd set of branches are for the test results. Suppose a woman has a positive Pap Smear test result, what are the chances that she actually has cervical cancer?

Use the info from the tree diagram that you created in Question#19

.

0.6804

b.

0.00283

c.

0.81

d.

0.000354

e.

0.84

Answer 1

Contingency table based on given information:

True Disease
No disease	Disease
P(D)=0.99992	P(D)=0.00008
0.99992	0.00008
Test positive	Test negative	Test positive	Test negative
19.00%	81.00%	84.00%	16.00%
False Positive	True Negative	True positive	False negative
0.1899848	0.8099352	0.0000672	0.0000128

P( has cancer / pap smear is positive) = Predictive postive value

PPV = Ture positive / (True positive + False postive) = 0.0000672 / (0.0000672 + 0.1899848)

P( has cancer / pap smear is positive) = 0.000354