I think the null hypothesis is “the neutrino detector is lying” because the question we are most interested in is if it is correctly telling us the sun has gone nova. If H0 is the null hypothesis and u1 is the chance of a neutrino event and u2 is the odds of double sixes then H0 = µ1 - µ2. Since the odds of two die coming up sixes is vastly larger than the odds of the sun going nova in our lifetime the test is not fair.
Among candidate stars for going nova I would think you could treat it as a random event. But Sol is not a candidate and so doesn’t even make it into the sample set. So it’s a very badly constructed setup. It’s like looking for a needle in 200 million haystacks but restricting yourself only to those haystacks you already know it cannot be in. Or do I have that wrong.
I think the null hypothesis is “the neutrino detector is lying” because the question we are most interested in is if it is correctly telling us the sun has gone nova. If H0 is the null hypothesis and u1 is the chance of a neutrino event and u2 is the odds of double sixes then H0 = µ1 - µ2. Since the odds of two die coming up sixes is vastly larger than the odds of the sun going nova in our lifetime the test is not fair.
I don’t think one would simply ignore the dice, and what data is the frequentist drawing upon in the comic which specifies the null?
How about “the probability of our sun going nova is zero and 36 times zero is still zero”?
Although… continuing with the XKCD theme if you divide by zero perhaps that would increase the odds. ;)
Since the sun going nova is not a random event, strict frequentists deny that there is a probability to associate with it.
Among candidate stars for going nova I would think you could treat it as a random event. But Sol is not a candidate and so doesn’t even make it into the sample set. So it’s a very badly constructed setup. It’s like looking for a needle in 200 million haystacks but restricting yourself only to those haystacks you already know it cannot be in. Or do I have that wrong.
I’m going to try the Socratic method...
Is a coin flip a random event?
taboo random event.
it’s deterministic, but you don’t know how it will come out.