Chapter+9

Chapter9

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Unformatted text preview: Chapter 9 Hypothesis Testing Developing Null and Alternative Hypotheses Type I and Type II Errors Population Mean: σ Known Population Mean: σ Unknown Population Proportion Developing Null and Alternative Hypotheses Hypothesis testing can be used to determine whether a statement about the value of a population parameter should or should not be rejected. The null hypothesis, denoted by H0 , is a tentative assumption about a population parameter. The alternative hypothesis, denoted by Ha, is the opposite of what is stated in the null hypothesis. The alternative hypothesis is what the test is attempting to establish. Developing Null and Alternative Hypotheses • Testing Research Hypotheses • The research hypothesis should be expressed as the alternative hypothesis. • The conclusion that the research hypothesis is true comes from sample data that contradict the null hypothesis. Developing Null and Alternative Hypotheses • Testing the Validity of a Claim • Manufacturers’ claims are usually given the benefit of the doubt and stated as the null hypothesis. • The conclusion that the claim is false comes from sample data that contradict the null hypothesis. Developing Null and Alternative Hypotheses • Testing in Decision­Making Situations • A decision maker might have to choose between two courses of action, one associated with the null hypothesis and another associated with the alternative hypothesis. • Example: Accepting a shipment of goods from a supplier or returning the shipment of goods to the supplier Summary of Forms for Null and Alternative Hypotheses about a Population Mean s The equality part of the hypotheses always appears in the null hypothesis. In general, a hypothesis test about the value of a population mean µ must take one of the following must take one of the following three forms (where µ 0 is the hypothesized value of the population mean). H 0 : µ ≥ µ0 H a : µ < µ0 H 0 : µ ≤ µ0 H a : µ > µ0 H 0 : µ = µ0 H a : µ ≠ µ0 One­tailed One­tailed (lower­tail) One­tailed (upper­tail) Two­tailed Null and Alternative Hypotheses • Example: Metro EMS 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 service goal is to respond to medical emergencies with a mean time of 12 minutes or less. Null and Alternative Hypotheses • Example: Metro EMS The director of medical services wants to formulate a hypothesis test that could use a sample of emergency response times to determine whether or not the service goal of 12 minutes or less is being achieved. Null and Alternative Hypotheses Null and Alternative Hypotheses H0: µ < 1 2 Ha: µ > 1 2 The emergency service is meeting the response goal; no follow­up action is necessary. The emergency service is not meeting the response goal; appropriate follow­up action is necessary. where: µ = mean response time for the population of me...
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