We have often heard about the notion of a burden of proof or an 'onus'. In legal contexts it seems as if prosectors have the burden of proof to prove the guilt of the defendant. That is, we assume that the defendant is innocent unless the prosecutor has provided sufficient evidence to do otherwise. In scientific contexts, we can consider burden of proofs in terms of null hypothesis': when one asserts a claim $C$ we conduct an experiment and only accept $C$ if it falls within some boundary such that it is almost implausible that it is due to luck. Note that the scientific and statistical position is quite interesting in that we maintain a 'null hypothesis' which we assume to be correct unless there is contrary evidence that $C$ is true.
It is not obvious however what exactly is the null hypothesis or what I would like to call the base position. Condition the fairly standard example where a student has a 100 question multiple choice (4 choices each) test. It seems the null hypothesis is that the student is just going to guess thus the null hypothesis would be that the student will average (obviously probablility says this is an average) at around 25 marks. Thus we set some sort of significance level and say we'd accept the alternative hypothesis if the evidence is in favour of this alternative hypothesis and that the probability of this evidence being like this due to luck is less that the significance level. Excusing the element of judgement in terms of significance level, we focus on the discussion on the null hypothesis. It seems here that:
$N : \mu = 25$, whilst $A: \mu \not = 25$ where $A$ is the alternative hypothesis that the student is not just guessing. Now it is fairly obvious that once we have accepted the initial position of 'student is just guessing' then we can conclude that our base position is that the student will on average score 25 marks. The question here is why do we assume that the student is just going to guess? How about a situation where we assume that a student who studied adequately would score $75$? It seems that we would also be able to take as a null hypothesis that $\mu = 75$ and that the alternative hypothesis would be a student did not study adequately and scored less than 75. The assumption of this null hypothesis seems to depend on the context of the situation. That is, it is not necessarily obvious that in any given situation there is only one null hypothesis. Should we null hypothesis that a student is guessing or should we null that they studied and hence their answers are not guesses? Does it make a difference if the one proposing the test claims either position? Does this affect who gets the priveledge of the null hypothesis?
