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A test to distinguish between a null hypothesis and an alternative hypothesis. For example, one may wish to test whether or not a coin is fair. The null hypothesis is that the coin is fair, and the alternative hypothesis is that it is biased. If a series of coin tosses produces a result that is only 3% likely given a fair coin, one would reject the null hypothesis, assuming 95% confidence is required. If, by contrast, the experiment produces a result that is 20% likely given a fair coin, one would fail to reject the null hypothesis that the coin is fair. It is not permissible to accept the alternative hypothesis. Only acceptance or failure to reject the null hypothesis is allowed in hypothesis testing. If a test fails to reject the null hypothesis, it is said to lack sufficient power to accept the alternative hypothesis. See also Type I Error, Type II Error.
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