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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 ttest 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 (onesided test) 2. H A : μ > μ (onesided test) 3. H A : μ 6 = μ (twosided 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 pvalue: P (  T  >  t  ) for the twosided test; P ( T > t ) or P ( T < t ) for the appropriate onesided test. Step 6: Choose α probability of type I error: α = P (reject H  H is true) . Typically α = 0 . 01 , . 05 . If pvalue 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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 Spring '09
 ALYAOTHMAN
 Statistics, Probability, Rafal Kulik

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