On October 23rd, 2014, we updated our
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The null hypothesis is that Population M 1 = Population M 2
If the null hypothesis is true, the two population means from which the samples are drawn are the same.
The population variances are estimated from the sample scores.
The variance of the distribution of differences between means is based on estimated population variances.
The goal of a t test for independent means is to decide whether the difference between means of your two actual samples is a more extreme difference than the cutoff difference on this distribution of differences between means.