sLecture4dPBS1 - Lecture #4 Learning Objectives Inference...

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Lecture #4 Learning Objectives Inference about μ when σ is known and X is Normal 1. Be able to determine power and the probability of making a Type II Error. 2. Know what a power curve and an operating characteristics (OC) curve are. 3. Be able to determine the size of a simple random sample required when the significance level and power are specified. 4. Know the definition of the following terms: Null Hypothesis Alternative Hypothesis Type I Error Type II Error Power Sample Size α β Operating Characteristics Curve Power Curve “A single death is a tragedy; a million deaths is a statistic.” - Joseph Stalin (1879 - 1953)
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BM330 – Lecture 4 1 Hypothesis Testing – Power and Errors When examining the usefulness of a confidence interval , we are concerned with • The level of confidence, C = (1 – α ): • The margin of error: When conducting hypothesis (significance) tests we are concerned with • The level of significance, α = max P(Type I error): • The likelihood of detecting (or failing to detect) an “effect” Power: Type II error: Decision Table Probabilities : Decision Concerning H 0 TRUE STATE OF THE WORLD H 0 Is True H 0 Is False Do not Reject H 0 1 - α β Reject H 0 α 1 - β
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BM330 – Lecture 4 2 Example 1 : Consider the following null and alternative hypotheses. H 0 : μ 100 H a : μ < 100 Suppose that the relevant population is Normal, σ = 5, α = 0.05, and n = 25. What is the Power of this test to detect that the population mean less than 100 when μ is really 99? Z 0 X How do you interpret this number? Do Not Reject H 0 (Insignificant) Reject H 0 α = 0.05 Z c = 1.645 0 _________________________________________________________ X c x = 98.355 μ 0 = 100 c x = 98.355 99 = μ a ______________________________________Z a 0.65 Power = .2578 α , σ , n , and μ 0 c X c X , μ a , σ , n Z a → Power What is this area?
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BM330 – Lecture 4 3 Example 2 – Medical Emergency Services Problem
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This note was uploaded on 02/22/2009 for the course BUSMGT 330m taught by Professor Kriska during the Spring '08 term at Ohio State.

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sLecture4dPBS1 - Lecture #4 Learning Objectives Inference...

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