Lecture25 - ECO220Y Lecture25 Hypothesis Testing (2) Migiwa...

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ECO220Y Lecture25 CO220 ectu e25 Hypothesis Testing (2) Migiwa Tanaka Reading: 11.2 (pp 349-352) 1
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utline Outline Testing population mean when the population variance is known Two Approaches to Hypothesis Testing Rejection Region Method p-value Method ne il vs two il Test One-tail vs. two-tail Test Calculating the probability of a type II error 2
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Statistical Inference: Inference of population mean μ hen known when σ is known .4 Population 1 Sampling Distribution Theory: l M ?? ? 2 .3 .6 .8 Sample Mean n i X X 1 σ is known .1 . .2 i n 1 ? ? ? 0 A Sample, n=50 μ A μ B μ C Sampling .15 ty The calculated (realized) mple mean: .05 Densi t n i x x 1 sample mean: 3 i n 1
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asic tuition f Hypothesis Testing Basic Intuition of Hypothesis Testing Consider one-tailed tests in this lecture. ppose e hypothesized that true population mean is 19 Suppose we hypothesized that true population mean is 19. H 0 : µൌ19 H 1 µ൐19 Scenario 1: We took a sample and obtained the sample mean =100. Very far away from the hypothesized value=19. x Reject null hypothesis in favor of alternative. Scenario 2: We take a sample and obtained the sample mean =21 ery ose to ypothesized value=19. x Very close to hypothesized value 19. Do not reject null hypothesis. How can we judge the calculated sample mean is far away or close pothesized one? to hypothesized one? 1 19 100 21 4
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rocedure of Hypothesis Testing Procedure of Hypothesis Testing Step 1: Construction of null hypothesis – presumption about population parameter (distribution)–and alternative ep 2: Collect a sample Step 2: Collect a sample Step 3: Consider that the null hypothesis is true.
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This note was uploaded on 03/01/2011 for the course ECON 220 taught by Professor Tanaka during the Spring '11 term at University of Toronto- Toronto.

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Lecture25 - ECO220Y Lecture25 Hypothesis Testing (2) Migiwa...

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