Slide 1Independent Versus Dependent SamplesDependent SamplesExample of Two PopulationsConstructing a Confidence Interval for µ1 - µ2Finding the Pair of Z ValuesSlide 7Hypothesis Testing for µ1 and µ2 (Large Samples)Ace Delivery ExampleSlide 10Slide 11Z Curve of Rejection RegionZ Curve with p-ValueIndependent Sample Tests for µ1 and µ2Independent Sample Tests for µ1 and µ2Two-Sample Procedure for Any Specified Value of µ1 - µ2Slide 17Two-Sample Z TestTest Statistic for µ1 - µ2 (Independent Samples) not assuming equal sigmasConfidence Interval for µ1 - µ2 (Independent Samples)Hypothesis Testing for µ1 - µ2 (Independent Samples)Slide 22Slide 23Two-Sample t TestTwo-Sample t TestTwo-Sample t TestEqual VariancesSlide 28Two-Tailed t TestSlide 30Slide 31Two-Tailed t TestTwo-Tailed t TestComparing Variances AssumptionsComparing VariancesSlide 36Slide 37Using The F-Statistic TableSlide 39Slide 40Hypothesis Test for 1 and 2Slide 42Allied Manufacturing ExampleConfidence Interval for 12/22Slide 45Comparing Paired, Dependent SamplesConfidence IntervalComparing MeansComparing MeansComparing MeansPaired Sample Tests for µdSlide 52Assumptions Behind ANOVADeriving the Sum of SquaresThe ANOVA TableTukey’s Multiple Comparison Test©2006 Thomson/South-Western 1Chapter 11 –Chapter 11 –Comparing Comparing Two or More Two or More PopulationsPopulationsSlides prepared by Jeff HeylLincoln University©2006 Thomson/South-WesternConcise Managerial StatisticsConcise Managerial StatisticsKVANLIPAVURKEELINGKVANLIPAVURKEELING©2006 Thomson/South-Western 2Independent VersusIndependent VersusDependent SamplesDependent SamplesIndependent SamplesIndependent SamplesThe occurrence of an observation in the first The occurrence of an observation in the first sample has no effect on the value(s) in the sample has no effect on the value(s) in the other sampleother sampleDependent Samples or paired samplesDependent Samples or paired samplesThe occurrence of an observation in the first The occurrence of an observation in the first sample has an impact on the corresponding sample has an impact on the corresponding value in the second samplevalue in the second sample©2006 Thomson/South-Western 3 Dependent SamplesDependent SamplesComparisons of before versus afterComparisons of before versus afterComparisons of people with matching Comparisons of people with matching characteristicscharacteristicsComparisons of observations matched Comparisons of observations matched by locationby locationComparison of observations matched Comparison of observations matched by timeby time©2006 Thomson/South-Western 4µµ1111Population 1Population 1µµ2222Population 2Population 2Figure 11.1Figure 11.1Example of Two PopulationsExample of Two Populations©2006 Thomson/South-Western 5For large samples where For large samples where ’s are known’s are knownZ Z ==((XX11 - - XX22) - (µ) - (µ11 - µ - µ22)) 22 22 nn11 nn22++1122The The (1 - (1 - ) • 100) • 100 confidence interval confidence interval22 22 nn11 nn22++1122((XX11 - - XX22) - ) - ZZ/2/2 to ( to (XX11 - - XX22) + ) + ZZ/2/222 22 nn11 nn22++1122Constructing a ConfidenceConstructing a Confidence Interval for Interval for µµ11 - µ - µ22©2006 Thomson/South-Western 6Finding the Pair of Z ValuesFinding the Pair of Z Values Figure 11.2Figure 11.2-1.645-1.645ZZ.05 .05 = 1.645= 1.645ZZArea = .90Area = .90Area = .45Area = .45Area = .45Area = .45Area = . 5 - .45 = .05Area = . 5 - .45 = .05Area = . 5 - .45 = .05Area = . 5 - .45 = .05©2006 Thomson/South-Western 7Example of Two PopulationsExample of Two Populations Figure 11.3Figure 11.3µµ22Male height Male height (population 2)(population 2)µµ11Female heights Female heights (population 1)(population 1)©2006 Thomson/South-Western 8Approximate the standard Approximate the standard normal random variable:normal random variable:Z Z ==((XX11 - - XX22)) 22 22 nn11 nn22++1122 Hypothesis Testing for Hypothesis Testing for µµ11 and and µµ22 (Large Samples) (Large Samples)©2006 Thomson/South-Western 9Ace Delivery ExampleAce Delivery Example1.1.Define the hypothesisDefine the hypothesisHHoo: µ: µ11 ≤ µ ≤ µ22(Texgas is less expensive)(Texgas is less expensive)HHaa: µ: µ11 > µ > µ22(Quik-Chek is less expensive)(Quik-Chek is less expensive)2.2.Define the test statisticDefine the test statisticZ Z ==((XX11 - - XX22)) 22 22 nn11 nn22++1122Example 11.2Example 11.2©2006 Thomson/South-Western 10Ace Delivery ExampleAce Delivery Example3.3.Define the rejection regionDefine the rejection regionreject reject HHoo if Z > 1.645 if Z > 1.6454.4.Evaluate the test statistic and carry out the testsEvaluate the test statistic and carry out the testsZZ * * = = = 3.50= = = 3.50((XX11 - - XX22)) 22 22 nn11 nn22++1122(1.48 - 1.39)(1.48 - 1.39) (.12)(.12)22 (.10) (.10)22 35 4035 40++Example 11.2Example 11.2©2006 Thomson/South-Western 11Ace Delivery ExampleAce Delivery Example5.5.State the conclusionState the conclusionQuik-Chek stores do charge less for gasoline Quik-Chek stores do charge less for gasoline (on the average) than do the Texgas stations(on the average) than do the Texgas stationsExample 11.2Example 11.2©2006 Thomson/South-Western 12Z Curve of Rejection RegionZ Curve of Rejection RegionFigure 11.4Figure 11.4ZZkk = 1.645= 1.645Area = .05Area = .05Area = . 5 - .05 = .45Area = . 5 - .05 = .45©2006 Thomson/South-Western 13 Z Curve with p-ValueZ Curve with p-ValueFigure 11.5Figure 11.5ZZ ** = 3.50= 3.50ZZAreaArea= = pp= .5 - .4998= .5 - .4998= .0002= .0002From Table A.4, From Table A.4, area = .4998area = .4998©2006 Thomson/South-Western 14Independent Sample Tests Independent Sample Tests for for µµ11 and and µµ22 Two-Tailed TestTwo-Tailed TestHHoo: µ: µ11 = µ = µ22HHaa: µ: µ11 ≠ µ ≠ µ22RejectReject HHOO if | if |ZZ| > | > ZZ/2/2wherewhereZ Z ==((XX11 - - XX22)) 22 22 nn11 nn22++1122©2006 Thomson/South-Western 15Independent Sample Tests Independent Sample Tests for for µµ11 and and µµ22One-Tailed TestOne-Tailed TestHHoo: µ: µ11 ≤ µ ≤ µ22HHaa: µ: µ11 > µ > µ22RejectReject HHoo if if ZZ > > ZZHHoo: µ: µ11 ≥ µ ≥ µ22HHaa: µ: µ11 < µ <
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