Biometry Ch 5 Sokal & Rohlf...

#1
I am unsure how to proceed with problem 5.5 in Biometry, Third Ed., pg. 96. The problem is as follows:

The Army Medical Core is concerned over the intestinal disease, Hershey Squirts. From previous experience, they know that soldiers suffering from the disease invariably harbor the pathogenic organism in their feces and that, for all practical purposes, every diseased stool specimen contains these organisms. The organisms are never abundant, however, and thus only 20% of all slides prepared by the standard procedure contain some of them (we assume that if an organism is present on a slide, it will be seen). How many slides per stool specimen should the laboratory technicians prepare and examine to ensure that if a specimen is positive, it will be erroneously diagnosed negative in less than 1% of the cases (on average)? On the basis of your answer, would you recommend that the Corps attempt to improve their diagnostic methods?

My answer thus far - Based on the percentage of slides given (20%), out of every 100 slides prepared, 20 would show up as infected. Only one slide is necessary to show infection however, so the percentage should hold true whether 10 slides, 100 slides, or 1000 slides were prepared. Preparing 10 slides would, on average, show 2 slides with the organism present. However, due to chance alone, some samples of 10 slides would show no organisms present. We would like the number of slides it would take to be reasonably sure we had this kind of error less than 1% of the time. Our population is all of the slides that could be prepared from one stool. Sokal’s given answer is 21 slides. Technically, one out of every 5 slides should show a positive. But again, due to chance, it seems likely to me that batches of 5 slides would be more prone to false negatives.

Problem - without a mean, I cannot see how to use a Poisson distribution for the rare event (false negative). Without data, I cannot see how to use a binomial distribution with this sample set. This course is independent study and I am bouncing around Chapter 5 trying to find some direction...any ideas??
 
#2
Answer...

I've got it now.

p=chance of finding organism
q=chance of not finding organism

p+q=1
Since q is the probability that the organism is not found, and we are interested in being sure less than 1% of the time, then the expansion is q raised to the 21st power, or 0.8 to the 21. This gives us a probability of about 0.009, less than a 1/100 chance. However, this means that at least 21 slides are needed. Too many to be of real value as a screening technique.

Since it took a week to get no reply to this post, and I think this answer was actually relatively straight-forward, I think this site is not going to be of any value in doing my homework. I am signing off permanently. Cheers.;|