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Unformatted text preview: Chapter 9 Hypothesis Testing Outline: • Develop Null Hypothesis and Alternative Hypothesis • Type I and Type II errors • OneTailed Tests about population mean: Large Sample Case • TwoTailed 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) 2 A major west coast city provides one of the most comprehensive emergency medical services in the world. Operating in a multiple hospital system with approximately 20 mobile medical units, the city has maintained the service goal to respond to medical emergencies with a mean time of 12 minutes or less. In a recent survey, a group of residents believed that the average response time had been longer than 12 minutes because of high demand in the last several months. In order to find out whether the belief was true, a sample of 40 response times was collected, and the average response time was 13.25 minutes with a standard deviation of 3.2 minutes for this sample. Null and Alternative Hypotheses • Null Hypothesis, Ho • An assertion about a population parameter • True until we have sufficient evidence to conclude otherwise • What is tested • Alternative Hypothesis, Ha • Opposite of what is stated in the null hypothesis • The burden of proof lies with Ha Define µ =the average response time 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 ). • The statement of the null hypothesis always contains an equal sign regarding the specified value of the parameter (such as, H : μ = 12). • The statement of the alternative hypothesis never contains an equal sign regarding the specified value of the parameter (such as, H a : μ > 12, or H a : μ ≤12, or H a : μ ≠ 12). 3 4 Example: Testing Research Hypotheses The research hypothesis should be expressed as the alternative hypothesis....
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 Spring '08
 Priya

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