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Hypothesis Testing 2

# Hypothesis Testing 2 - MAT2378 Rafal Kulik Version...

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Unformatted text preview: MAT2378 Rafal Kulik Version 2009/Oct/30 Rafal Kulik MAT2378 Probability and Statistics for the Natural Sciences Hypothesis PART 2 Comments • These notes form an introduction to hypotheses testing. They do not correspond to any section in the textbook . • I’m planning to spend one lecture on this material. Rafal Kulik 1 MAT2378 Probability and Statistics for the Natural Sciences Hypothesis PART 2 The t-test We are going to test H : μ = μ , where μ is a constant. Step 1: H : μ = μ In the second step we choose an alternative H A : Step 2: Choose H A as one of 1. H A : μ < μ (one-sided test) 2. H A : μ > μ (one-sided test) 3. H A : μ 6 = μ (two-sided test) Rafal Kulik 2 MAT2378 Probability and Statistics for the Natural Sciences Hypothesis PART 2 Step 3: The test statistics T = ¯ Y- μ S/ √ n . This statistics has t n- 1 under H . Step 4: Compute the observed value t = ¯ y- μ s/ √ n of your test statistics. Step 5: Compute the p-value: P ( | T | > | t | ) for the two-sided test; P ( T > t ) or P ( T < t ) for the appropriate one-sided test. Step 6: Choose α- probability of type I error: α = P (reject H | H is true) . Typically α = 0 . 01 , . 05 . If p-value is smaller than α- reject H . Rafal Kulik 3 MAT2378 Probability and Statistics for the Natural Sciences Hypothesis PART 2 The form of hypotheses will depend on what we try to show or to conclude. As alternative, we choose what we try to demonstrate by data....
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Hypothesis Testing 2 - MAT2378 Rafal Kulik Version...

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