Editing Alternative hypothesis (section)

==Example==
One example is where water quality in a stream has been observed over many years, and a test is made of the null hypothesis that "there is no change in quality between the first and second halves of the data", against the alternative hypothesis that "the quality is poorer in the second half of the record".

If the [[statistical hypothesis testing]] is thought of as a judgement in a court trial, the null hypothesis corresponds to the position of the defendant (the defendant is innocent) while the alternative hypothesis is in the rival position of prosecutor (the defendant is guilty). The defendant is innocent until proven guilty, so likewise in a hypothesis test, the null hypothesis is initially [[Presumption|presumed]] to be true. To prove the statement of the prosecutor, evidence must be convincing enough to convict the defendant; this is analogous to sufficient [[statistical significance]] in a hypothesis test. 

In the court, only legal evidence can be considered as the foundation for the trial. As for hypothesis testing, a reasonable [[test statistic]] should be set to measure the statistic significance of the null hypothesis. Evidence would support the alternative hypothesis if the null hypothesis is rejected at a certain significance level. However, this does not necessarily mean that the alternative hypothesis is true due to the potential presence of a [[type I error]]. In order to quantify the statistical significance, the test statistic variables are assumed to follow a certain probability distribution such as the [[normal distribution]] or [[Student's t-distribution|t-distribution]] to determine the probability of obtaining test results at least as extreme as the [[Realization (probability)|results actually observed]], under the assumption that the [[null hypothesis]] is correct, which is defined as the [[p-value|''p''-value]].<ref>{{Cite journal|date=2015-11-24|title=Which scientists can winningly explain a flame, time, sleep, color, or sound to 11-year-olds?|url=http://dx.doi.org/10.1063/pt.5.8150|journal=Physics Today|doi=10.1063/pt.5.8150|issn=1945-0699 |last1=Corneliussen |first1=Steven T. |issue=11 |page=11792 |bibcode=2015PhT..2015k1792C |url-access=subscription }}</ref><ref>{{Cite journal|last1=Wasserstein|first1=Ronald L.|last2=Lazar|first2=Nicole A.|date=2016-04-02|title=The ASA Statement on p -Values: Context, Process, and Purpose|journal=The American Statistician|language=en|volume=70|issue=2|pages=129–133|doi=10.1080/00031305.2016.1154108|s2cid=124084622 |issn=0003-1305|doi-access=free}}</ref> If the p-value is smaller than the chosen [[significance level]] (''α''), it can be claimed that observed data is sufficiently inconsistent with the [[null hypothesis]] and hence the null hypothesis may be rejected. After testing, a valid claim would be "at the significance level of (''α''), the [[null hypothesis]] is rejected, supporting the alternative hypothesis instead". In the metaphor of a trial, the announcement may be "with tolerance for the probability ''α'' of an incorrect conviction, the defendant is guilty."