When performing a hypothesis test of a difference of two proportions, does one change the integrity of the problem when changing the scale?
To clarify: I want to test the difference in proportions of maintenance errors per hour of maintenance for two sets of years, say A = [1990-2000] and B = [2000-2010]. When I did this, I found that I had 4 errors from set A and 4 errors from set B. I also found that I had about 2000 maintenance hours in set A and about 2500 maintenance hours in set B. This does not meet the "rule of thumb" for using the normal distribution in a CI of proportions. Also, I've been told that the n = 2000 is far to greater than x = 4 for the proportion x/n. (Same for y and m).
Are there any general methods to combat this? Does it change the integrity of the problem if I just change the scale from maintenance hours, to days of maintenance? (2000/24 = 83.3 so use 4/83.3 instead of 4/2000)
Sorry if this is unclear, I tried to explain it the best I could. I can't find any literature on this.