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In reporting the result of a significance test, showing the observed test statistic and its location in the null distribution along with the tail area is a helpful and frequently used graphic. This Demonstration makes it easy to construct this plot for the one-sample test for the population mean of a normal distribution. The effect of sample size, the assumption that the population variance is known or not, as well the question of using a one-sided or two-sided test may also be explored. Let ... be the sample mean of ... observations in a random sample from a normal population with mean ... and standard deviation ... . The ... -value for testing ... against one of the alternatives ... , ... or ... is illustrated using tests based on the test statistic ... when ... is assumed known, and ... when ... is not known, where ... , ... and ... is the sample standard deviation. The ... -value for the test is shown by the shaded area. When the tail area is smaller than 5%, a red arrow is used to indicate the position of the test statistic. The null distribution for ... and ... are respectively the standard Gaussian and Student ... on ... degrees of freedom. So when ... is known, the slider for ... is disabled.
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