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IEOR 165 Lecture 5 June 3 2009

# IEOR 165 Lecture 5 June 3 2009 - Lecture Notes IEOR 165 |...

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Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry New topic: Hypothesis Testing Recap: So far, introduce different confidence intervals & distributions. Then MOM & MLE. (1) Say something about population behavior (2) Collect data & characterize the population. (3) Estimate the parameters by MOM or MLE Hypothesis Testing example: Someone claims something is true & we verify if the statement is right or wrong E.g. Avg UCB SAT score is 1440. Prove/disprove. E.g. Consulting salary is 120k So we randomly sample data. Big Question: How do we verify data? Answer: We find the 99% confidence interval for the mean salary. If 120k is within this confidence interval, then it may be true. After proving/disproving, we need to give an alternative conclusion. E.g. mean is > or < 120k. (1) Test for population Mean Population x with unknown mean = [ ] μ E x Somebody claims that = μ μ0 where μ0 is a numerical value specified. (2) Objective: Verify this claim. (3) To do this, we first consider an alternative hypothesis / prove that it’s wrong. 3 possibilities: - Case 1: μ μ0 - : < Case 2 μ μ0 - : > Case 3 μ μ0 - - Case 1: - Null Hypothesis: = μ μ0 ( ) H0 - Alternative hypothesis: μ μ0 H1 - - Sample data: , …, x1 xn - Consider - % . . 1 α100 C I for μ - * , + * , x zα2 σn x zα2 σn if σ is known - , - * , + , - * , x tα2 n 1 sn x tα2 n 1 sn if σ is unknown

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Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry - Suppose , . . μ0 is NOT CI μ is not inside the C I THEN we reject H0 in favor of H1 - - Suppose , μ0 CI we do not have enough evidence to reject H0 So We Accept H0against H1 - - - - - Case 2: - Null Hypothesis: = μ μ0 ( ) H0 - Alternative hypothesis: > μ μ0 H1
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