11.4 Statistical Hypothesis Tests for the Difference of Means When Sampling from Two Independent Normal Populations
Let 
and 
be random samples taken from independent normal distributions with means μX and μY and variances 
and 
, respectively. Our objective is to test the difference between the two population means μX and μY, where this difference will be denoted as 
. So if μX = μY, then δo = 0; if μX > μY, then δo > 0; and if μX < μY, then δo < 0. In this regard, we may test the null hypothesis 
against any one of the following three alternative hypotheses:
| Case 1 | Case 2 | Case 3 |
 |
 |
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