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A t-test is a statistical hypothesis test based on a test statistic whose sampling distribution is a t-distribution. Various t-tests, strictly speaking, are aimed at testing hypotheses about populations with normal probability distribution. However, statistical research has shown that t-tests often provide quite adequate results for non-normally distributed populations too.

The term “t-test” is often used in a narrower sense – it refers to a popular test aimed at testing the hypothesis that the population mean is equal to some value m (see also t-statistic).

The most popular t-tests are aimed at testing the following hypotheses:

1) The population mean is as hypothesized (the population variance is not known).

2) The means of two populations are equal (the population variances are not known but equal).

3) The means of two populations are equal (the population variances are not known and not equal).

4) The correlation coefficient for two random variables is zero.

5) The slope of the population regression line is zero.

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