ioe265f11-Lec18 - IOE 265 F11 - Hypothesis Testing Overview...

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IOE 265 F11 - Hypothesis Testing Overview Luis Guzman, Univ of Michigan 1 1 Hypothesis Tests 2 Topics I. Statistical Hypothesis Null and Alternative Hypothesis Testing statistics and rejection regions II. Errors in Hypothesis Testing Type I and II errors
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IOE 265 F11 - Hypothesis Testing Overview Luis Guzman, Univ of Michigan 2 3 I. Statistical Hypothesis Statistical Hypothesis - claim about the value of a single population parameter/characteristic (e.g. mean, variance), or relationship between several population characteristics. Examples of Claims: Mean diameter of an 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, H 0 Claim that is initially assumed to be true. Alternative Hypothesis, Ha Assertion that is contradictory to H 0 . Null Hypothesis is rejected if sample evidence suggests that it is false. If not false, we fail to Reject H 0 . So, possible outcomes of test are: Reject H 0 Or Fail to Reject H NOTE: fail to reject Ho is different from saying that we have proven H 0 is true.
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IOE 265 F11 - Hypothesis Testing Overview Luis Guzman, Univ of Michigan 3 5 “Favored Claim” In setting up a test, we typically have a favored claim which is the H 0 . Familiar analogy: innocent until proven guilty. Practical examples: Suppose you want to fire a worker for non-performance. H 0 : 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. H
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ioe265f11-Lec18 - IOE 265 F11 - Hypothesis Testing Overview...

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