Many researchers wish to test a statistical hypothesis with their data.
There are several preparations we make before we observe the data. For example, The mean response to treatment being tested is equal to the mean response to the placebo in the control group. Both response have the Normal Distribution with the unknown means and the same known Standard Deviation . A test Statistic must be chosen that will summarize the information in the sample that is relevant to the hypothesis. In the example given above, it might be the numerical difference between the two sample means, m 1 -m 2 .