M203E Homework 25, due Wed Nov 9, 2011

[1] The teenage pregnancy rate in 2006 was 72/1000; i.e., 72 teenage girls were pregnant 
on average out of every 1000 teenage girls (http://www.guttmacher.org/pubs/USTPtrends.pdf). 
Home pregnancy kits (for women who collect 
and test their own samples) was found to have an overall sensitivity of 75% and a specificity of 
around 65% (http://www.medicine.ox.ac.uk/bandolier/band64/b64-7.html). The sensitivity means 
that among pregnant women, the test will correctly identify the pregnancy in 75% (or 3 of 4) cases, 
and the specificity means that among women who are not pregnant, the test will correctly 
identify 65% (or about 2 out of every 3) as not being pregnant.

Given a random sample of 10000 teen girls, fill in the following table with the appropriate numbers:
----------------------------------------------------------------------------------------
                         |   girls who are    |     girls who are     |   row totals   |
                         |   pregnant         |     not pregnant      |                |
----------------------------------------------------------------------------------------
Test is positive         |                    |                       |                |
(indicating pregnancy)   |                    |                       |                |
                         |                    |                       |                |
----------------------------------------------------------------------------------------
                         |                    |                       |                |
Test is negative         |                    |                       |                |
(indicating no pregnancy)|                    |                       |                |
                         |                    |                       |                |
----------------------------------------------------------------------------------------
                         |                    |                       |                |
column totals            |                    |                       |     10000      |
                         |                    |                       |                |
----------------------------------------------------------------------------------------

(a) If a pregnant teen uses one of these home pregnancy kits, what's the chance that it 
will correctly say she is pregnant?

(b) If a pregnant teen uses one of these home pregnancy kits, what's the chance of a false 
negative (i.e., that it will incorrectly say she is not pregnant)?

(c) If a teen who is not pregnant uses one of these home pregnancy kits, what's the chance 
that it will correctly say she is not pregnant?

(d) If a teen who is not pregnant uses one of these home pregnancy kits, what's the chance 
of a false positive (i.e., that it will incorrectly say she is pregnant)?

(e) If a randomly chosen teen uses one of these home pregnancy kits and gets a negative result, 
what's the chance it is a false negative (i.e., what's the chance she is pregnant in spite of 
the test saying she's not)?