Hi! So, yours is actually a sophisticated question that masquerades as a simple one, so I'll try to answer this in a way that conveys the concept while perhaps alluding to some of its problems. At its heart, the null hypothesis is a sort of "straw man" that is defined by a researcher at the beginning of an experiment that usually represents a state of affairs that would be expected to occur if the researcher's proposal were false. Note that a null hypothesis is entirely imaginary, and it has nothing to do with the actual state of the world. It is contrived, usually to show that the actual state of the world is inconsistent with the null hypothesis. Suppose a researcher is trying to determine whether the heights of men and women are different. A suitable null hypothesis might be that the difference of the two population averages (height of men and height of women) is equal to zero. Then the researcher would conduct his or her experiment by measuring the heights of many men and women. When it comes time to draw a statistical conclusion, he or she will compute the probability that the observed data (the set of heights) could have come from the null hypothesis (i.e., a world where there is no difference). This probability is called a "p-value". Conceptually, this is similar to a "proof by contradiction," in which we assert that, if the probability is very small that the data could have originated from the null hypothesis, it must not be true. This is what is meant by "rejecting the null hypothesis". It is different from a proof by contradiction because rejecting the null proves nothing, except perhaps that the null is unlikely to be the source of the observed data. It doesn't prove that the true difference is 5 inches, or 1 inch, or anything. Because of this, rejecting the null hypothesis is in NO WAY equivalent to accepting an alternative hypothesis. Usually, in the course of an experiment, we observe a result (such as the observed height difference, perhaps it is ~5 inches) that, once we reject, replaces the hypothesized value of 0 under the null. However, we DON'T know anything about the probability that our observed value is "correct", which is why we never say that we have "accepted" an alternative. I actually hesitate to discuss an "alternative" hypothesis because most researchers never state one and it doesn't matter for the purposes of null hypothesis significance testing (NHST). It is just the name given to the conclusion drawn by the researchers after they have rejected their null hypothesis. Philosophically, there is an adage that data can never be used to prove an assertion, only to disprove one. It includes an analogy about a turkey concluding that he is loved by his human family and is proven wrong upon being slaughtered on Thanksgiving. I'll include a link if I can find it. Now, think about this: The concept of rejecting a null hypothesis probably seems very reasonable as long as we are careful not to overinterpret it, and this is how NHST was performed for decades. But consider - what is the probability that the null hypothesis is true in the first place? In other words, how likely is it that the difference between mens' and womens' heights is equal to zero? I propose that the probability is exactly zero, and if you disagree then I will find a ruler small enough to prove me correct. The difference can never be equal to exactly zero (even though this is the "straw man" that our experiment refutes), so we are effectively testing against a hypothesis that can never be true. Rejecting a hypothesis we already know to be false tells us nothing important ("the data are unlikely to have come from this state that cannot be true"). And since every null hypothesis is imaginary, it is suggested that any null hypothesis can be rejected with enough statistical power (read:sample size). Often a "significant" result says more about a study's sample size than it does about the study's findings, even though the language used in papers/media suggests to readers that the findings are more "important" or "likely to be correct". This has, in part, led to a reproducibility crisis in the sciences and, for some, an undermining of subject-matter-experts' trust in the use of applied statistics. More on reddit.com

The Null in Null Hypothesis just means that there is no hypothesis. The Null Hypothesis is just the status quo and and the Alternative Hypothesis is what you are trying to gather evidence for. Because we are starting with a reasonable assumption as the status quo, we look to reject that assumption. Or we fail to gather enough evidence to reject that assumption. EDIT for an example: Let's say you claim to be psychic and you want to perform an experiment to prove it by guessing the outcome of 100 coin flips. What's the reasonable assumption here? What's the status quo? The reasonable assumption is that you are not psychic, because that's a thing that doesn't exist, you don't need proof that someone is not psychic. So the null hypothesis would be be that you will not correctly guess more coin flips than would be expected by random chance alone, but the alternative hypothesis would be that you will correctly guess a number of flips that's highly unlikely to be done by random, say more than 3 standard deviations from the mean. More on reddit.com

You have to think about the epistemology of statistical inference. We are trying to see if we can find "evidence to support a theory". The only way to do that in frequentist stats is to "find evidence inconsistent with another theory". So, if you want to see if "there is evidence to support a positive relationship", you have to see if there is evidence inconsistent with the idea that there is a negative or zero relationship. One of the important factors in digesting this is to realize that if you "fail to reject a null hypothesis", that, in itself, is not evidence that the null is true (many repeated, independent tests with sufficient power that fail to reject will make us "comfortable" with that null...). Regarding equality in the alternate: Since all hypothesis tests must state a specific numerical idea to compare to, you must have an equality statement in the null. The idea behind all hypothesis tests is to try to quantify how inconsistent your data are with the null. If your null has no equality, then which of the uncountably infinite unequal values are you comparing your data to? More on reddit.com

There is a chance that your drug being tested doesn't work. However the 2 groups of people - one get the real drug, one gets the placebo - are not identical. We aim to get a "fair" representation of the population by having a lot of people. On average this works out to be close enough to identical over the large group.... But sometimes it doesn't work out. Sometimes there are more smokers in group A than in group B. Sometimes there are more people with a family history of heart attacks in group A than group B. And so on. So there is a chance that your drug did nothing and your placebo group are just unhealthy to begin with compared to your real drug group. The Null hypothesis makes you ask the question "did the drug do nothing and we got screwed by luck?". You can usually quantify this as a probability. How likely is it that these results are bad luck? A small number like 0.01% means yeah, you can probably reject the null hypothesis and hence your drug was good. A number like 20% and it's a lot less convincing that your drug was the deciding factor. More on reddit.com