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Definition: Hypothesis Testing is a statistical method of reasoning and decision making using data from a scientific study.
The question of interest is simplified into two competing claims / hypotheses between which we have a choice; the null hypothesis (H0) against the alternative hypothesis (H1).
These two competing claims / hypotheses are not however treated on an equal basis: special consideration is given to the null hypothesis.
Statistical hypothesis tests define a procedure which controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect based on how likely it would be for a set of observations to occur if the null hypothesis were true.