On 24 Nov 2003 07:47:39 -0800, [EMAIL PROTECTED] (Find_Housing) wrote: > Hi! > > I came accross this statistics issue and am hoping to get some > suggestions from here. As part of our experiment design we have a need > to statistically quantify the number of bacteria in a bag of medium. > The goal is to be able to say that the bag is bacteria-free after > evaluating some sampels taken from the bag.
This problem becomes easier when it is stated right. Your goal is to say that the bag is *practically* bacteria-free; it need to be bacteria-free for *practical* purposes. How small is small enough? The super-pasteurized milk can 'keep' at room temperature because the total count in a quart has been reduced to dozens of organisms or less. >From there, it will take months for the growth to become hazardous. What is your limit? Are you groping blindly, or is there something formally stated? > The size of the total medium is 50 ml for the bag and the volume of > sample taken for evaluation is 0.5 ml. Okay, there could be 100 samples. Here is amplification of my point above, to show that proving 'zero' is impractical. If you test 50 samples, what is the chance that exactly 1 of the original 100 samples had 1 bacterium? => 50%. There is only a 50-50 chance that you would have picked the 'bad' one in your sample. This is something that works out pretty generally: If you want to prove that something is zero, and the alternative is one, then you don't even make much progress by "random sampling" until you have sampled a large portion. What can save infinite sampling, for one thing, is sampling that is *not* random but has a biased chance. What you really need for your application, though, is a small, non-zero amount that is acceptable. You can only push the estimated proportion *toward* zero, if you are making an accurate estimate. [ snip, detail not yet relevant] -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html "Taxes are the price we pay for civilization." . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
