Each member of the first sample must be paired with a member of the second sample, and both samples must be drawn at random from a normal population.
The samples are separate and at random. It is unknown what the population standard deviations are. Either the populations are regularly distributed or both samples have sample sizes of at least 30.
Hypotheses for the two-sample t test
A valid test requires independent data values. One observation's measurements have no bearing on any other observation's measurements. Each group's data must be collected from the population using a random sampling.
The scale of measurement, random sampling, normality of data distribution, appropriate sample size, and equality of variance in standard deviation are some of the frequent presumptions made while conducting a t-test.
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