Alternative Hypothesis (from Internet Glossary of Statistical Terms)

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Alternative Hypothesis
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The test of a given statistical hypothesis entails an assessment of whether or not our sample (or samples) have yielded a statistic that is among those cases that would only occur α proportion of the time if the hypothesis tested is true.

In these circumstances we know the probability of rejecting the hypothesis tested when it is true (that probability is equal to α) but unless we have also specified an alternative hypothesis to the hypothesis tested, we have no idea of the probability of being in error, if our test has failed to yield a value that enables us to reject the hypothesis tested.