Graphical Relationship Signs in Alternative Hypothesis

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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