Definition: an Alternative Hypothesis or H1 is a statement in hypothesis testing of what the statistical hypothesis test is set up to establish.
For example, in a clinical trial of a new drug, the alternative hypothesis might be that the new drug has a different effect, on average, compared to that of the current drug:
H1: the two drugs have different effects, on average.
The alternative hypothesis might also be that the new drug is better, on average, than the current drug. In this case we would write:
H1: the new drug is better than the current drug, on average.
The final conclusion once the test has been carried out is always given in terms of the null hypothesis.
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