Chapter 9 Hypothesis TestingDeveloping Null and Alternative HypothesesSlide 3Slide 4Slide 5Slide 6Null and Alternative HypothesesSlide 8Slide 9Type I ErrorSlide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Example: Glow ToothpasteSlide 29Slide 30Slide 31Slide 32Slide 33Slide 34Confidence Interval Approach to Two-Tailed Tests About a Population MeanSlide 36Tests About a Population Mean: s UnknownSlide 38p -Values and the t DistributionExample: Highway PatrolSlide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53End of Chapter 91 1 Slide Slide© 2006 Thomson/South-Western© 2006 Thomson/South-WesternChapter 9Chapter 9 Hypothesis Testing Hypothesis Testing Developing Null and Alternative HypothesesDeveloping Null and Alternative Hypotheses Type I and Type II ErrorsType I and Type II Errors Population Mean: Population Mean:  Known Known Population Mean: Population Mean:  Unknown Unknown Population ProportionPopulation Proportion2 2 Slide Slide© 2006 Thomson/South-Western© 2006 Thomson/South-WesternDeveloping Null and Alternative Developing Null and Alternative HypothesesHypotheses Hypothesis testingHypothesis testing can be used to determine whether can be used to determine whether a statement about the value of a population parametera statement about the value of a population parameter should or should not be rejected.should or should not be rejected. The The null hypothesisnull hypothesis, , denoted by denoted by HH0 0 , , is a tentativeis a tentative assumption about a population parameter.assumption about a population parameter. The The alternative hypothesisalternative hypothesis, denoted by , denoted by HHaa, is the, is the opposite of what is stated in the null hypothesis.opposite of what is stated in the null hypothesis. The alternative hypothesis is what the test isThe alternative hypothesis is what the test is attempting to establish.attempting to establish.3 3 Slide Slide© 2006 Thomson/South-Western© 2006 Thomson/South-WesternTesting Research HypothesesTesting Research HypothesesDeveloping Null and Alternative Developing Null and Alternative HypothesesHypotheses• The research hypothesis should be expressed asThe research hypothesis should be expressed as the alternative hypothesis.the alternative hypothesis.• The conclusion that the research hypothesis is trueThe conclusion that the research hypothesis is true comes from sample data that contradict the nullcomes from sample data that contradict the null hypothesis.hypothesis.4 4 Slide Slide© 2006 Thomson/South-Western© 2006 Thomson/South-WesternDeveloping Null and Alternative Developing Null and Alternative HypothesesHypothesesTesting the Validity of a ClaimTesting the Validity of a Claim• Manufacturers’ claims are usually given the benefitManufacturers’ claims are usually given the benefit of the doubt and stated as the null hypothesis.of the doubt and stated as the null hypothesis.• The conclusion that the claim is false comes fromThe conclusion that the claim is false comes from sample data that contradict the null hypothesis.sample data that contradict the null hypothesis.5 5 Slide Slide© 2006 Thomson/South-Western© 2006 Thomson/South-WesternTesting in Decision-Making SituationsTesting in Decision-Making SituationsDeveloping Null and Alternative Developing Null and Alternative HypothesesHypotheses• A decision maker might have to choose betweenA decision maker might have to choose between two courses of action, one associated with the nulltwo courses of action, one associated with the null hypothesis and another associated with thehypothesis and another associated with the alternative hypothesis.alternative hypothesis.• Example: Accepting a shipment of goods from aExample: Accepting a shipment of goods from a supplier or returning the shipment of goods to thesupplier or returning the shipment of goods to the suppliersupplier6 6 Slide Slide© 2006 Thomson/South-Western© 2006 Thomson/South-WesternOne-tailedOne-tailed(lower-tail)(lower-tail)One-tailedOne-tailed(upper-tail)(upper-tail)Two-tailedTwo-tailed0 0: H 0 0: H 0: aH 0: aH 0 0: H 0 0: H 0: aH 0: aH 0 0: H 0 0: H 0: aH 0: aH Summary of Forms for Null and Summary of Forms for Null and Alternative Hypotheses about a Alternative Hypotheses about a Population MeanPopulation Mean The equality part of the hypotheses always appearsThe equality part of the hypotheses always appears in the null hypothesis.in the null hypothesis. In general, a hypothesis test about the value of aIn general, a hypothesis test about the value of a population mean population mean must take one of the followingmust take one of the following three forms (where three forms (where 00 is the hypothesized value of is the hypothesized value of the population mean).the population mean).7 7 Slide Slide© 2006 Thomson/South-Western© 2006 Thomson/South-WesternExample: Metro EMSExample: Metro EMSNull and Alternative HypothesesNull and Alternative Hypotheses Operating in a multipleOperating in a multiplehospital system with hospital system with approximately 20 mobile medicalapproximately 20 mobile medicalunits, the service goal is to respond to medicalunits, the service goal is to respond to medicalemergencies with a mean time of 12 minutes or less.emergencies with a mean time of 12 minutes or less. A major west coast city providesA major west coast city providesone of the most comprehensiveone of the most comprehensiveemergency medical services inemergency medical services inthe world.the world.8 8 Slide Slide© 2006 Thomson/South-Western© 2006 Thomson/South-Western The director of medical servicesThe director of medical serviceswants to formulate a hypothesiswants to formulate a hypothesistest that could use a sample oftest that could use a sample ofemergency response times toemergency response times todetermine whether or not thedetermine whether or not theservice goal of 12 minutes or lessservice goal of 12 minutes or lessis being achieved.is being achieved.Example: Metro EMSExample: Metro EMSNull and