Graphical Relationship Signs in Alternative Hypothesis
I have attached P.173 and all of chapter 12 if you need it
Chapter 12 of Froister & Blessing (pp. 173) discusses one-tailed and two-tailed t-tests. Statisticians characteristically include the equal-sign component in the null Hypothesis (H0). This means that the null hypothesis of a two-tailed-test of two means would appear as:
H0: (Mean)1 = (Mean)2 with alternative hypothesis H1: (Mean)1 ≠ (Mean)2.
Had we created a one-tailed-test of means, the null and alternative hypotheses would appear as:
H0: (Mean)1 ≤ (Mean)2 with H1: (Mean)1 > (Mean)2, or
H0: (Mean)1 ≥ (Mean)2 with H1: (Mean)1 < (Mean)2.
What is the graphical relationship of the signs in the alternative hypothesis to the area of rejection of the null hypothesis?
What are Type I and Type II errors? Why should we care?
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