<P> The p - value is the probability that a given result (or a more significant result) would occur under the null hypothesis . For example, say that a fair coin is tested for fairness (the null hypothesis). At a significance level of 0.05, the fair coin would be expected to (incorrectly) reject the null hypothesis in about 1 out of every 20 tests . The p - value does not provide the probability that either hypothesis is correct (a common source of confusion). </P> <P> If the p - value is less than the chosen significance threshold (equivalently, if the observed test statistic is in the critical region), then we say the null hypothesis is rejected at the chosen level of significance . Rejection of the null hypothesis is a conclusion . This is like a "guilty" verdict in a criminal trial: the evidence is sufficient to reject innocence, thus proving guilt . We might accept the alternative hypothesis (and the research hypothesis). </P> <P> If the p - value is not less than the chosen significance threshold (equivalently, if the observed test statistic is outside the critical region), then the evidence is insufficient to support a conclusion . (This is similar to a "not guilty" verdict .) The researcher typically gives extra consideration to those cases where the p - value is close to the significance level . </P> <P> Some people find it helpful to think of the hypothesis testing framework as analogous to a mathematical proof by contradiction . </P>

Hypothesis testing is best described as which of the following