PROBLEM 1: if instead of sampling 5, I sample a 1000, then the probability of observing 3 dead RPs and 2 OK RPs (under H0) is: ${1000 \choose 600} (3/5)^{600} (1-3/5)^{400} = 0.026$....!!! This -too- is statistically significant? But how can it be, it's just the null hypothesis itself, except for observing a larger sample.

PROBLEM 1: if instead of sampling 5, I sample a 1000, then the probability of observing 3:5 dead to OK RPs (under H0) is: ${1000 \choose 600} (3/5)^{600} (1-3/5)^{400} = 0.026$....!!! This -too- is statistically significant? But how can it be, it's just the null hypothesis itself, except for observing a larger sample.

PROBLEM 1: if instead of sampling 5, I sample a 1000, then the probability of observing 3 dead RPs and 2 OK RPs (under H0) is: ${1000 \choose 600} (3/5)^360 (1-3/5)^240 = 0.026$....!!! This -too- is statistically significant? But how can it be, it's just the null hypothesis itself, except for observing a larger sample.

PROBLEM 1: if instead of sampling 5, I sample a 1000, then the probability of observing 3 dead RPs and 2 OK RPs (under H0) is: ${1000 \choose 600} (3/5)^{600} (1-3/5)^{400} = 0.026$....!!! This -too- is statistically significant? But how can it be, it's just the null hypothesis itself, except for observing a larger sample.

PROBLEM 1: if instead of sampling 5, I sample a 1000, then the probability of observing 3 dead RPs and 2 OK RPs (under H0) is: ${1000 \choose 600} (3/5)^360 (1-3/5)^240 = 0.026$....!!! This -too- is statistically significant? But how can it be, it's just the null hypothesis itself, except for observing a larger sample.

GUESS 2: I guess we must somehow normalize the $p$ value of the observation against the maximum likelihood that is $p=0.026$. Right?