You don't prove the null hypothesis. But you might not have enough evidence to rule it out.
I don't honestly know how to apply this kind of t-test logic to the question of whether gods exist, but I think we have fairly adequate evidence that dodo birds do not exist any more, and we haven't even tried that hard. If you try very very hard and in good ways to find something which by all rights should be there, and don't find it, it's just basic honesty to say you 'failed to reject the null hypothesis' than to make plausible excuses about how it really must exist despite the dearth of evidence.
If you have an idea about how to really find it, then it's up to you to make a better methodology and then use it to find the thing. And you can keep coming up with better and better methodologies around all the excuses for as long as you want to. Everyone can.
But the more sustained and general the failure to see expected evidence, the less likely the basis of the expectation. So rational people will give up on Eldorado and Shangri-la after many attempts fail to find any evidence for them. Shangri-la might be hiding behind a cloud, sure, but that doesn't mean that every claim is equally credible. A million excuses for lack of evidence are more likely a product of human frailties than of the claim actually being true after all that failure to support it.
I don't honestly know how to apply this kind of t-test logic to the question of whether gods exist, but I think we have fairly adequate evidence that dodo birds do not exist any more, and we haven't even tried that hard. If you try very very hard and in good ways to find something which by all rights should be there, and don't find it, it's just basic honesty to say you 'failed to reject the null hypothesis' than to make plausible excuses about how it really must exist despite the dearth of evidence.
If you have an idea about how to really find it, then it's up to you to make a better methodology and then use it to find the thing. And you can keep coming up with better and better methodologies around all the excuses for as long as you want to. Everyone can.
But the more sustained and general the failure to see expected evidence, the less likely the basis of the expectation. So rational people will give up on Eldorado and Shangri-la after many attempts fail to find any evidence for them. Shangri-la might be hiding behind a cloud, sure, but that doesn't mean that every claim is equally credible. A million excuses for lack of evidence are more likely a product of human frailties than of the claim actually being true after all that failure to support it.