Originally Posted by scorcherjf
A confidence interval can be calculated at any percentage given you have a mean and a standard deviation which can be done with as little as 3 observations. The confidence interval will be very bad and not very significant, but it can be calculated nonetheless.
To the OP:
Lets say each "observation" is a petri dish. Each observation has an outcome of 0 or 1. 0 meaning no growth, 1 for any kind of growth. You run this test with n trials and compute the mean and standard deviation. You can then calculate the 95% confidence intervals. To calculate the confidence interval you need to use a student T-distribution table to lookup the value corresponding to the percentage you want given how many observations you have, n.
For example, if you had 100 petri dishes and only 1 of them had growth while the other 99 had no growth, the mean would simply be 1/n=0.01 and the standard deviation would be 0.1. The null hypothesis is that the mean should be 0.001 meaning 1 out of every 1000 petri dishes will have growth according to the manufacturer's claim of 99.9%. To calculate the test statistic you need to subtract the hypothesized mean from the sample mean and then divide by the standard deviation. In this example it would be (0.01 - 0.001)/0.1 = 0.9. Look up what percentage 0.9 falls under on the student-t table for n-1=99 degrees of freedom. This would correspond to roughly around 70% confidence so at the 95% confidence level you cannot reject the null hypothesis of the mean of 0.001 (manufacturer's claim).
What you're most likely going to find is none of your petri dishes with the treatment will have growth so the standard deviation will be 0 and you will have to conclude that the mean is in fact 0 and you'll be unable to calculate any intervals since there was no variation in the results.
I might've lead you down a totally incorrect path so sorry if I did but I hope it helps a little. (There are some more pedantic points like calculating sample mean and sample standard deviation to take into account degrees of freedom but I think that's beyond the scope of this...)
Actually on second thought this wouldn't even work... as I said before you need a non-binary continuous set of outcomes for this to work... ideally you'd have each sample report a percentage of bacteria killed so your data would look something like [99.1, 99.3, 98.7, etc] and then take the mean and standard deviation of that to compute the confidence intervals.
FML...you're right....i'll talk to the statistician at my medschool to get this designed properly...i still feel very ignorant!
4.0 in science and math in college including honors calc and stats...lol