27 - BUAD 310: Applied Business Statistics September 27,...

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September 27, 2010 BUAD 310: Applied Business Statistics 1
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Outline for Today Hypothesis testing Null and alternative hypotheses Type I and II errors Test statistic and P-value Hypothesis testing process 2
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A Quick Review Statistical inference: Estimation Point estimate: sample mean and sample proportion (Chapter 14) Interval estimate: confidence interval (CI) (Chapter 15) Hypothesis testing 3
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Confidence intervals are used when the goal is to estimate a population parameter (e.g. μ or p ) with a certain precision Another approach to statistical inference is hypothesis testing – making decisions based on partial information (from a sample) Introduction to hypothesis testing 4
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Null and Alternative Hypotheses 5 Similar to a courtroom trial. In trying a person for a crime, the jury needs to decide between one of two possibilities: The person is guilty. The person is innocent. To begin with, the person is assumed innocent. The prosecutor presents evidence, trying to convince the jury to reject the original assumption of innocence, and conclude that the person is guilty.
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Null and Alternative Hypotheses The null hypothesis, H 0 : The hypothesis we wish to falsify Assumed to be true until we can prove otherwise. The alternative hypothesis, H a : The hypothesis we wish to prove to be true 6 Court trial: H 0 : innocent H a : guilty
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One-Sided and Two-Sided 7 Need to set up two hypotheses, H 0 and H a Two-sided tests: concerned with deviations from H 0 in either direction H 0 : μ = μ 0 versus Ha: μ ≠ μ 0 One-sided tests: concerned with deviations from H 0 in only one direction H 0 : μ ≤ μ 0 versus H a : μ > μ 0 or H 0 : μ ≥ μ 0 versus H a : μ < μ 0
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One-Sided or Two-Sided? The choice between a one-sided and two-sided test can be controversial A two-sided test is the more conservative choice and should be used unless there is very good reason to prefer a one-sided test 8
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Trash bag case: a marketer of trash bags uses hypothesis testing to support its claim that the mean breaking strength of its new trash bag is greater than 50 pounds. H 0 : μ ≤ 50 H a : μ > 50 ( One-Sided, Greater Than) Payment time case: a consulting firm uses hypothesis testing to provide strong evidence that the new electronic billing system has reduced the mean payment time by more than 50 percent (i.e., the new mean is less than 39/2 = 19.5 days). H 0 : μ ≥19.5 H a : μ < 19.5 ( One-Sided, Less Than ) Camshaft case: an automobile manufacturer uses hypothesis testing to study an important quality characteristic affecting V6 engine camshafts. It finds that the mean “hardness depth” significantly differs from its desired target value of 4.5mm. H
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27 - BUAD 310: Applied Business Statistics September 27,...

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