Lecture11 - March 15th Chapter 6(continued Hypothesis...

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March 15th Chapter 6 (continued) Hypothesis Testing Example. 0 H ( null hypothesis ) : the average height is 5’8” or more. 0 ( : 5'8") H μ a H ( alternative hypothesis ) : the average height is less than 5’8” ( : 5'8") a H μ p Example . (law suit) O.J. Simpson case 0 H : O.J. is innocent. ( original belief ) a H : O.J. is guilty. Truth 0 H a H Decision 0 H Correct Decision Type II error a H Type I error Correct Decision 0 0 (Type I error) (Reject | ) P P H H α = = This probability is called the significance level of the test . Scenario 1 : Inference on one population mean μ (normal population, 2 σ is known) There are two methods. 1. Pivotal Quantity Method (We will learn this method first.) 2. Likelihood Ratio Test (We will learn this method later.) 1
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Now we introduce the general procedures in the Pivotal Quantity method. 1. Before deriving the test, you must know your Pivotal Quantity for the given problem: ~ (0,1) X Z N n μ σ - = 2. Now you can start your hypothesis test. First write down your hypotheses. There are 3 cases (or choices). You need to choose the one that is most suitable for your given problem. a. (one-sided test) 0 0 0 0 0 0 : or equivalently, : : : a a H H H H μ μ μ μ μ μ μ μ = f f b. (one-sided test) 0 0 0 0 0 0 : or equivalently, : : : a a H H H H μ μ μ μ μ μ μ μ = p p c. (two-sided test) 0 0 0 : : a H H μ μ μ μ = In the following we introduce the remainder of the test derivation procedures for each pair of hypotheses.
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