Chapter 9 Notes

Chapter 9 Notes - Chapter 9 Hypothesis Testing Outline •...

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Unformatted text preview: Chapter 9 Hypothesis Testing Outline: • Develop Null Hypothesis and Alternative Hypothesis • Type I and Type II errors • One-Tailed Tests about population mean: Large Sample Case • Two-Tailed Tests about population mean: Large Sample Case • Tests about population mean: Small Sample Case • Tests about Population Proportion What is Hypothesis? 1 2 Null and Alternative Hypotheses: • Null Hypothesis: H – An assertion about the population parameter (μ = 50 in the example) – True until we have sufficient evidence to prove otherwise – Think of as the claim being tested • Alternative Hypothesis: H a – Opposite of what was said in null hypothesis – What requires evidence to prove • Hypothesis testing and criminal trial – H : The defendant is innocent – H a : The defendant is guilty (considered innocent unless proved guilty) Three forms of hypothesis: About a population mean Note that the equality part of the hypothesis is always part of the null hypothesis. 2 Example: Testing Research Hypotheses Consider a particular automobile model that currently attains an average fuel efficiency of 24 miles per gallon. A product research group has developed a new fuel injection system to increase the mpg rating. The product research group is looking for evidence to conclude that the new system increases the mean mpg rating. a. Develop the null and alternative hypotheses that are most appropriate for this study. b. What conclusion is appropriate when H can be rejected? Example: Testing the validity of a claim A manufacturer of soft drinks states that two-liter containers of its products have an average of at least 67.6 fluid ounces . A sample of two-liter containers will be selected, and the contents will be measured to test the manufacturer’s claim . a. What are H and H a ? b. What conclusion is appropriate when H can be rejected? 3 4 Example: Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of \$220 per hour. State the appropriate null and alternative hypotheses. Summary of Null and Alternative Hypotheses: • The null hypothesis ( H ) is the hypothesis that is tested. • The alternative hypothesis ( H a ) is set up as the opposite of the null hypothesis and represents the conclusion supported if the null hypothesis is rejected. • The null hypothesis always refers to a specified value of the population parameter (such as μ ), not a sample statistic (such as )....
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Chapter 9 Notes - Chapter 9 Hypothesis Testing Outline •...

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