| Problem Set |
Section |
Problems |
|---|---|---|
| 18 | 7.7 | Read this section |
| ∗1 | The book uses the following numbers one in a thousand (r = 0.001) people in the U.S. is infected with AIDS. the lab test for AIDS has a false positive rate of 1 percent (0.01). the lab test for AIDS has a false negative rate of 5 percent (0.05). From this information, they calculate the probability a person has the disease given he has tested positive as being about 9 percent (really more like 0.086, or 8.6 percent). All of these rates have changed since the writing of the book. In particular, about one in 301 people in the U.S. is infected with AIDS. (source until.org | nationmaster.com) the lab test for AIDS has a false positive rate between 0.000004 and 0.000007. (source wikipedia.org) the lab test for AIDS has a false negative rate of about 0.00003. Use these figures to calculate an updated probability of being positive for AIDS when you have tested positive for it. (Since there is a range of possible values for the false positive rate, choose the one that gives the worst-case scenario---the greatest probability.) Hint: For those of you who were in class to see a formula derived for this type of calculation, you might first use the book numbers and see if your calculation leads to the book figure of 0.086, just to be sure you are using the formula correctly. |
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| 7.7(I) | 6 -- Blonde, bleached blonde | |
| 9 -- Pocket change | ||
| 10 -- Random person | ||
| 11 -- Another random person | ||
| ∗2 | Re-read the part of Section 7.6 dealing with “Embarrassing Questions” (pp. 584-587). What similarities do you see between the procedures for obtaining truthful numbers of people who have done something embarrassing to admit and the procedure for determining the probability of having AIDS given you tested positive for it? | |
| n | manditory problem |
| (n) | helper problem |
| [n] | ungraded problem |
| {n} | optional problem |