Chapter 9 Hypothesis Testing

Chapter 9Hypothesis TestingCopyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinHypothesis Testing9.1 Null and Alternative Hypotheses and Errors in Testing9.2 z Tests about a Population Meanσ Known9.3 t Tests about a Population Meanσ Unknown9.4 z Tests about a Population Proportion9.5 Type II Error Probabilities and Sample Size Determination (Optional)9-*9.1 Null and Alternative Hypotheses and Errors in Hypothesis TestingNull hypothesis, H0, is a statement of the basic proposition being testedRepresents the status quo and is not rejected unless there is convincing sample evidence that it is falseAlternative hypothesis, Ha, is an alternative accepted only if there is convincing sample evidence it is trueOne-Sided, “Greater Than” H0: μ  μ0 vs. Ha: μ > μ0One-Sided, “Less Than” H0 : μ  μ0 vs. Ha : μ ρ0z > zaArea under t distribution to right of zHa: ρ z a/2 *Twice area under t distribution to right of |z|Where the test statistics is* either z > zα/2 or z µ0 or Ha: µ ≠ µ0Want to make the probability of a Type I error equal to α and randomly select a sample of size nLO9-6: Calculate Type II error probabilities andthe power of a test, and determine sample size (Optional).9-*Calculating β ContinuedThe probability β of a Type II error corresponding to the alternative value µa for µ is equal to the area under the standard normal curve to the left of Here z* equals zα if the alternative hypothesis is one-sided (µ µ0)Also z* ≠ zα/2 if the alternative hypothesis is two-sided (µ ≠ µ0)LO9-69-*