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Lecture Business statistics in practice (7/e): Chapter 9 - Bowerman, O'Connell, Murphree

Chapter 9 - Hypothesis testing. After mastering the material in this chapter, you will be able to: Set Up appropriate null and alternative hypotheses, describe Type I and Type II errors and their probabilities, use critical values and p-values to perform a z test about a population mean when s is known,. | Chapter 9 Hypothesis Testing Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Hypothesis Testing 9.1 Null and Alternative Hypotheses and Errors in Testing 9.2 z Tests about a Population Mean σ Known 9.3 t Tests about a Population Mean σ Unknown 9.4 z Tests about a Population Proportion 9.5 Type II Error Probabilities and Sample Size Determination (Optional) 9- 9.1 Null and Alternative Hypotheses and Errors in Hypothesis Testing Null hypothesis, H0, is a statement of the basic proposition being tested Represents the status quo and is not rejected unless there is convincing sample evidence that it is false Alternative hypothesis, Ha, is an alternative accepted only if there is convincing sample evidence it is true One-Sided, “Greater Than” H0: μ μ0 vs. Ha: μ > μ0 One-Sided, “Less Than” H0 : μ μ0 vs. Ha : μ Hypothesis Testing 9.1 Null and Alternative Hypotheses and Errors in Testing 9.2 z Tests about a Population Mean σ Known 9.3 t Tests about a Population Mean σ Unknown 9.4 z Tests about a Population Proportion 9.5 Type II Error Probabilities and Sample Size Determination (Optional) 9- 9.1 Null and Alternative Hypotheses and Errors in Hypothesis Testing Null hypothesis, H0, is a statement of the basic proposition being tested Represents the status quo and is not rejected unless there is convincing sample evidence that it is false Alternative hypothesis, Ha, is an alternative accepted only if there is convincing sample evidence it is true One-Sided, “Greater Than” H0: μ μ0 vs. Ha: μ > μ0 One-Sided, “Less Than” H0 : μ μ0 vs. Ha : μ 9- Types of Decisions As a result of testing H0 vs. Ha, will decide either of the following decisions for the null hypothesis H0: Do not reject H0 or reject H0 To “test” H0 vs. Ha, use the “test statistic” z measures the distance between μ0 and x on the sampling distribution of the sample mean If the population is normal or n is large*, the test statistic z follows a normal distribution LO9-1 9- Error Probabilities Type I Error: Rejecting H0 when it is true is the probability of making a Type I error 1 – is the probability of not making a Type I error Type II Error: Failing to reject H0 when it is false β is the probability of making a Type II error 1 – β is the probability of not making a Type II error LO9-2: Describe Type I and Type II errors and their probabilities. Table 9.1 9- Typical Values Usually set to a low value So there is a small chance of rejecting a true .