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Statistical Inference: A Short Course by Michael J. Panik

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11.4 Statistical Hypothesis Tests for the Difference of Means When Sampling from Two Independent Normal Populations

Let img and img be random samples taken from independent normal distributions with means μX and μY and variances img and img, respectively. Our objective is to test the difference between the two population means μX and μY, where this difference will be denoted as img. 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 img against any one of the following three alternative hypotheses:

Case 1 Case 2 Case 3
img img img

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