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What is a null hypothesis?

What is a null hypothesis? Here are some definitions.

Noun
  1. (statistics) A hypothesis set up to be nullified or refuted in order to support an alternative hypothesis. When used, the null hypothesis is presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. Therefore, the null and the alternative hypothesis must be mutually exclusive and exhaustive. The use of the null hypothesis is controversial.
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Examples
Paup does not reproduce the phenetic clusters, and therefore the null hypothesis is falsified.
The next step in hypothesis testing is to draw a conclusion based on the decision to reject or not reject the null hypothesis.
A null hypothesis can either be accepted or it can be rejected in favour of an alternative hypothesis.
We performed significance tests of the null hypothesis of constant population size for both data sets.
There is a potential misuse of the power function under the logical extreme when the null hypothesis is true.
If the null hypothesis is rejected, the program calculates a posterior probability for functional divergence for each position in the alignment.

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