hypothesis testing: A better fly killer Say I have to prove that a new fly killer is better than an existing one and I set up an experiment where I put both fly killers in a room of live flies and empty and count how many flies are killed by each fly killer every 10 minutes.
The fly killers don't interfere; the past number of flies killed does not affect the number of flies available for killing.
If I have counts of flies killed by each fly killer every 10 minutes, I can work out mean fly kills for each product and compare them, but how do I determine that I have enough samples to work out if any difference is significant?
What if I calculate standard deviations of the means for each fly killer, Can I use these to make a better statement of the validity of any statement that one is better than another?
I should just state that my statistical knowledge is not great, I am an engineer that found the term "hypothesis testing" just today when doing my own search.
Thanks.
 A: First, read up on the basics of hypothesis testing, i.e., Null vs Alternative Hypotheses, the role of the test statistic and rejection region, Type I vs Type II error. After that, you will want to model the number of flies caught every 10 minutes as a Poisson random variable with mean rate $\lambda$ flies per 10 minutes. Then, I think this post will answer your questions; https://stats.stackexchange.com/questions/9561/checking-if-two-poisson-samples-have-the-same-mean
A: What I have so far.
Assume normal distribution of flies killed by either flykiller.
Call the flykillers X and Y
I can calculate the mean and sd of the kill rates of each flykiller:
  Xmean, Xsd, Ymean, Ysd
From https://en.wikipedia.org/wiki/Cumulative_distribution_function it seems that we can use the cdf to calculate the probability "that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x"
So for any kill rate k shouldn't I be able to calculate the probability of X >= Y as:
(1 - cdf(k, Xmean, Xsd)) * cdf(k, Ymean, Xsd)
I.e. the probability that X > k times the probability that Y < k = probability that X >= Y
If we calculate the above for all k wouldn't we be able to get the maximum probability that X >= Y and 
as long as that probability is below a threshold, say 5% could I then go on to say that Y > X with 95% confidence?
