Editing Null hypothesis (section)

==Basic definitions==
The null hypothesis and the ''alternative hypothesis'' are types of [[Conjecture|conjectures]] used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise. 

The statement being tested in a test of [[statistical significance]] is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis, or a statement of 'no effect' or 'no difference'.<ref name=moore/> It is often symbolized as ''H''<sub>0</sub>.

The statement that is being tested against the null hypothesis is the alternative hypothesis.<ref name=moore/> Symbols may include ''H''<sub>1</sub> and ''H''<sub>a</sub>.

A statistical significance test starts with a random sample from a population. If the sample data are consistent with the null hypothesis, then you do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis, then you reject the null hypothesis and conclude that the alternative hypothesis is true.<ref>{{cite book|last=Weiss|first=Neil A.|title=Introductory Statistics|edition=5th|year=1999|page=[https://archive.org/details/introductorystat00neil/page/494 494]|publisher=Addison Wesley |isbn=978-0201598773|url=https://archive.org/details/introductorystat00neil/page/494}}</ref>

Consider the following example. Given the test scores of two random [[statistical sample|sample]]s, one of men and one of women, does one group score better than the other? A possible null hypothesis is that the mean male score is the same as the mean female score:

: ''H''<sub>0</sub>: ''μ''<sub>1</sub> = ''μ''<sub>2</sub>

where

: ''H''<sub>0</sub> = the null hypothesis,
: ''μ''<sub>1</sub> = the mean of population 1, and
: ''μ''<sub>2</sub> = the mean of population 2.

A stronger null hypothesis is that the two samples come from populations with equal variances and shapes of their respective distributions.  This is known as a pooled variance.