Lab assignment 5 (due Friday, March 3)

*** SLBD stands for the book "Statistics: Learning by Doing."  ***

*** SAWA stands for "Short Answer Writing Assignment"  ***

Please read lab session 10 (pages 142-155 of SLBD) BEFORE coming to class
on Monday.

Just scan this reading, because although the basic part of the experiment will 
be the same as in the book, we will change a lot of details and the analysis 
will vary from that described in the book.  You will be given a handout which 
gives the instructions for analyzing the data.

I.  Answer SAWA questions 1 through 8 (in complete sentences where appropriate) 
of the SAWA worksheet handed out in class.  (We will not use the SAWA questions 
in the lab book.)

II.  Devices which screen donated blood for the AIDS virus are subject to a small 
degree of error.  When presented with blood actually containing the AIDS virus, 
the test will yield a positive result 99 percent of the time.  When presented with 
blood which actually does not contain the virus, the test result will be positive 
2 percent of the time.  (This is known as the "false positive" rate.) 

(a) Suppose there are 12,000 blood samples, none of which has the AIDS virus.  If 
we apply the screening test to them, what is the mean number of (false) positive 
results?  [Hint:  Define "positive test result" as the success.  What is n here?  
What is p?]

(b) Suppose there are 12,020 blood samples, 12,000 of which are clean and 20 of 
which contain the virus.  We apply the test to all 12,020; what is the mean number 
of positive results? [Hint:  Break the experiment into two binomial experiments, 
one with n = 12,000 and one with n = 20.  Note that p will be different for the 
two situations.  Then add the means for each experiment to get the overall mean 
number of positives.]

(c) Out of the overall mean number of positive results, what percentage is the 
mean number of false positives?  What does this tell you about most positive 
results for tests (even if the test has a small error rate) for a rare disease?