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High Quality Content by WIKIPEDIA articles! The two-tailed test is a statistical test used in inference, in which a given statistical hypothesis , H0 (null hypothesis) will be rejected when the value of the statistic is either sufficiently small or sufficiently large. The test is named after the "tail" of data under the far left and far right of a bell-shaped normal data distribution, or bell curve. However, the terminology is extended to tests relating to distributions other than normal. If the distribution from which the samples are derived is considered to be normal, Gaussian, or bell-shaped, then the test is referred to as a one- or two-tailed T test. If the test is performed using the actual population mean and variance, rather than an estimate from a sample, it would be called a one- or two-tailed Z test.