ioe265f11-Lec21

# ioe265f11-Lec21 - Lec21 Hypothesis Testing Overview Main...

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Lec21 - Hypothesis Testing Overview IOE 265 F11 1 1 Hypothesis Tests Summary 2 Main Topics I. Statistical Hypothesis II. Errors in Hypothesis Testing III. Single Sample Tests IV. Two Sample Tests

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Lec21 - Hypothesis Testing Overview IOE 265 F11 2 3 I. Statistical Hypothesis Statistical Hypothesis - claim about the value of a single population characteristic, or relationship between several population characteristics. Examples of Claims: Mean diameter of the engine cylinder is 81 mm. Mean of batch 1 is no different than the mean of batch 2. Variance of batch 1 is different than the variance of batch 2. % Defective of batch 1 is less than 5%. In hypothesis testing, we take a sample of data and test a claim. 4 Null and Alternative Hypothesis To evaluate a claim, you identify a null and alternative hypothesis. Null Hypothesis, Ho Claim that is initially assumed to be true. Alternative Hypothesis, Ha Assertion that is contradictory to Ho. Null Hypothesis is rejected if sample evidence suggests that it is false. If not false, we fail to Reject Ho. So, possible outcomes of test are: Reject Ho Or Fail to Reject Ho NOTE: fail to reject Ho is different from saying that we have proven Ho is true.
Lec21 - Hypothesis Testing Overview IOE 265 F11 3 5 “Favored Claim” In setting up a test, we typically have a favored claim which is the Ho. Familiar analogy: innocent until proven guilty. Practical examples: Suppose you want to fire a worker for non-performance. Ho: worker is meeting the minimum job requirements. Ha: worker is not meeting the minimum job requirements. Suppose you want to know whether to rework a machine-tool. Ho: machine produces a part feature average on target. Ha: machine does not produce a feature average on target. 6 Statistical Hypothesis Tests Comparison of Means Single mean to a standard value Two sample means Comparison of Variances Single variance to a standard value Two sample variances Comparison of Proportions Single proportion to a standard value Two proportions

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Lec21 - Hypothesis Testing Overview IOE 265 F11 4 7 Test Procedures To perform a hypothesis test, you need: Null and Alternative Hypothesis An assumed data pattern / distribution (e.g., normal, iid) Test Statistic - function of the sample data on which the decision is based. Rejection region - set of test statistic values for which the Ho is rejected. (based on error threshold) 8 II. Errors in Hypothesis Testing Conclude Or Say Not Different Different Truth Not Different Different Type I Error  Type II Error  Power
Lec21 - Hypothesis Testing Overview IOE 265 F11 5 9 Definitions of Error Types Type I error [also known as alpha ( ) error] - FORMAL: Reject Ho when Ho is true PRACTICAL: Conclude a difference exists when no difference exists.

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## This note was uploaded on 01/05/2012 for the course IOE 265 taught by Professor Jin during the Fall '07 term at University of Michigan.

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ioe265f11-Lec21 - Lec21 Hypothesis Testing Overview Main...

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