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.
You have a sample of 10 students who were recruited to take part in the study. The researcher wants to see if the group who received the experimental procedure would perform any differently than those who did not receive any experimental procedure.
5 students were randomly assigned to the experimental group and 5 were randomly assigned to the control group.
All of the students rated their overall level of emotional adjustment on a scale from 0 (very poor) to 10 (very positive).