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I'm working through a stats textbook and have a question of the form:

You will perform a significance test of H0: μ=25 based on an SRS of n=25. Assume σ=5.

I'm stuck on the 'equals' part of μ=25. Given that we're working in the set of reals, isn't the probability of μ equaling 25 zero? (Assume a non-textbook dataset; e.g. the odds of μ=180 for the height of adult humans is zero).

I think what the hypothesis is trying to say is "μ is within bounds dictated by your confidence level, but mean(μ)=25".

The alternate hypothesis is something like "Ha: μ != 25", which I know is true for any non-hypothetical dataset.

So, what does "H0: μ=25" actually mean?

I'm working through a stats textbook and have a question of the form:

You will perform a significance test of $H_0: μ=25$ based on an SRS of $n=25$. Assume $σ=5$.

I'm stuck on the 'equals' part of $μ=25$. Given that we're working in the set of reals, isn't the probability of $μ$ equaling 25 zero? (Assume a non-textbook dataset; e.g. the odds of $μ=180$ for the height of adult humans is zero).

I think what the hypothesis is trying to say is "$μ$ is within bounds dictated by your confidence level, but mean$(μ)=25$".

The alternate hypothesis is something like $H_a: μ \neq 25$, which I know is true for any non-hypothetical dataset.

So, what does $H_0: μ=25$ actually mean?

I'm working through a stats textbook and have a question of the form:

You will perform a significance test of H0: μ=25 based on an SRS of n=25. Assume σ=5.

I'm stuck on the 'equals' part of μ=25. Given that we're working in the set of reals, isn't the probability of μ equalling 25 zero? (Assume a non-textbook dataset; e.g. the odds of μ=180 for the height of adult humans is zero).

I think what the hypothesis is trying to say is "μ is within bounds dictated by your confidence level, but mean(μ)=25".

The alternate hypothesis is something like "Ha: μ != 25", which I know is true for any non-hypothetical dataset.

So, what does "H0: μ=25" actually mean?

I'm working through a stats textbook and have a question of the form:

You will perform a significance test of H0: μ=25 based on an SRS of n=25. Assume σ=5.

I'm stuck on the 'equals' part of μ=25. Given that we're working in the set of reals, isn't the probability of μ equaling 25 zero? (Assume a non-textbook dataset; e.g. the odds of μ=180 for the height of adult humans is zero).

I think what the hypothesis is trying to say is "μ is within bounds dictated by your confidence level, but mean(μ)=25".

The alternate hypothesis is something like "Ha: μ != 25", which I know is true for any non-hypothetical dataset.

So, what does "H0: μ=25" actually mean?