Why does null hypothesis in simple linear regression (i.e. slope = 0) have distribution? I have been reading about simple linear regression ($y=wx+b$), and I started a section when it talks about null hypothesis $w=0$. Then, when it wants to calculate p-value, they use $t-score = \frac{\bar{w}-0}{SE}$, where SE is the standard error. What I do not understand is this fraction.
In z-score, we have $\frac{x-\mu}{\sigma}$, and $\mu$ and $\sigma$ are parameters of distribution. So, similarly, regarding the t-score, I should think that 0 and $SE$ are parameters of distribution (of null hypothesis. correct?). However, if the null hypothesis says the slope, $w$, is zero, why should I consider  a distribution for it? And, if there is a distribution, why is its spread parameter equal to $SE$, which is an estimation of standard deviation of $w$ (calculated based on alternative hypothesis)?
I tried to look at different articles and a couple of books, but whenever I get to this part, I still feel like something is missing.

The null hypothesis is nothing more than a specified value of the parameter of interest in the statistical model. It is the point in parameter space where $\omega=0$. (More completely, it is the line in parameter space where $\omega=0$ over the range of all possible $\beta$ values.) It is probably not helpful to think of it 'having a distribution'.
The things where we worry about distributions are typically populations and statistics such as the test statistic $t$. Within the statistical model (the equations and assumptions underlying the method) the test statistic has a known distribution so that you can compare the observed value of the statistic to that distribution. You can therefore see how 'extreme' the observed value is (i.e. how unexpected it is, or how strange it is) relative to its distribution.
The statistical model also allows determination of what the distribution of the test statistic would be if the 'true' value of the parameter of interest was any value other than the null hypothesis.
The assumptions relating to population distribution are usually necessary in order that the test statistic will have a particular known distribution.
If statistical model shows that the observed value of the test statistic would rarely be found under the null hypothesis then the data cast doubt on that null hypothesis.
