For the t distribution to apply strictly we need the following two assumptions:

**ASSUMPTIONS REQUIRED FOR t
DISTRIBUTION**

For the *t*
distribution to apply strictly we need the following two assumptions:

1. The observations are selected
at random from the population.

2. The population distribution is
normal.

Sometimes these assumptions may not be met
(particularly the second one). The *t*
test is robust for departures from the normal distribution. That means that
even when assumption 2 is not satisfied because the population differs from the
normal distribution, the probabilities calculated from the *t* table are still approximately correct. This outcome is due to
the central limit theorem, which implies that the sample mean will still be
approximately normal even if the observations themselves are not.

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