Chapter 10Comparisons Involving Means Part A商务统计 教学课件.ppt

《Chapter 10Comparisons Involving Means Part A商务统计 教学课件.ppt》由会员分享，可在线阅读，更多相关《Chapter 10Comparisons Involving Means Part A商务统计 教学课件.ppt（43页珍藏版）》请在三一办公上搜索。

1、Chapter 10 Comparisons Involving MeansPart A,Inferences About the Difference Between Two Population Means:s 1 and s 2 Known,Inferences About the Difference Between Two Population Means:Matched Samples,Inferences About the Difference Between Two Population Means:s 1 and s 2 Unknown,Inferences About t

2、he Difference BetweenTwo Population Means:s 1 and s 2 Known,Interval Estimation of m 1 m 2Hypothesis Tests About m 1 m 2,Estimating the Difference BetweenTwo Population Means,Let 1 equal the mean of population 1 and 2 equal the mean of population 2.,The difference between the two population means is

3、 1-2.,To estimate 1-2,we will select a simple random sample of size n1 from population 1 and a simple random sample of size n2 from population 2.,Let equal the mean of sample 1 and equal the mean of sample 2.,The point estimator of the difference between the means of the populations 1 and 2 is.,Expe

4、cted Value,Sampling Distribution of,Standard Deviation(Standard Error),where:1=standard deviation of population 1 2=standard deviation of population 2 n1=sample size from population 1 n2=sample size from population 2,Interval Estimate,Interval Estimation of 1-2:s 1 and s 2 Known,where:1-is the confi

5、dence coefficient,Example:Par,Inc.,Interval Estimation of 1-2:s 1 and s 2 Known,In a test of driving distance using a mechanicaldriving device,a sample of Par golf balls wascompared with a sample of golf balls made by Rap,Ltd.,a competitor.The sample statistics appear on thenext slide.,Par,Inc.is a

6、manufacturerof golf equipment and hasdeveloped a new golf ballthat has been designed toprovide“extra distance.”,Example:Par,Inc.,Interval Estimation of 1-2:s 1 and s 2 Known,Sample Size,Sample Mean,Sample#1Par,Inc.,Sample#2Rap,Ltd.,120 balls 80 balls,275 yards 258 yards,Based on data from previous d

7、riving distancetests,the two population standard deviations areknown with s 1=15 yards and s 2=20 yards.,Interval Estimation of 1-2:s 1 and s 2 Known,Example:Par,Inc.,Let us develop a 95%confidence interval estimateof the difference between the mean driving distances ofthe two brands of golf ball.,E

8、stimating the Difference BetweenTwo Population Means,m1 m2=difference between the mean distances,Point Estimate of 1-2,Point estimate of 1-2=,where:1=mean distance for the population of Par,Inc.golf balls2=mean distance for the population of Rap,Ltd.golf balls,=275-258,=17 yards,Interval Estimation

9、of 1-2:1 and 2 Known,We are 95%confident that the difference betweenthe mean driving distances of Par,Inc.balls and Rap,Ltd.balls is 11.86 to 22.14 yards.,17+5.14 or 11.86 yards to 22.14 yards,Hypothesis Tests About m 1-m 2:s 1 and s 2 Known,Hypotheses,Left-tailed,Right-tailed,Two-tailed,Test Statis

10、tic,Example:Par,Inc.,Hypothesis Tests About m 1-m 2:s 1 and s 2 Known,Can we conclude,usinga=.01,that the mean drivingdistance of Par,Inc.golf ballsis greater than the mean drivingdistance of Rap,Ltd.golf balls?,H0:1-2 0,where:1=mean distance for the population of Par,Inc.golf balls 2=mean distance

11、for the population of Rap,Ltd.golf balls,1.Develop the hypotheses.,p Value and Critical Value Approaches,Hypothesis Tests About m 1-m 2:s 1 and s 2 Known,2.Specify the level of significance.,a=.01,3.Compute the value of the test statistic.,Hypothesis Tests About m 1-m 2:s 1 and s 2 Known,p Value and

12、 Critical Value Approaches,p Value Approach,4.Compute the pvalue.,For z=6.49,the p value.0001.,Hypothesis Tests About m 1-m 2:s 1 and s 2 Known,5.Determine whether to reject H0.,Because pvalue a=.01,we reject H0.,At the.01 level of significance,the sample evidenceindicates the mean driving distance

13、of Par,Inc.golfballs is greater than the mean driving distance of Rap,Ltd.golf balls.,Hypothesis Tests About m 1-m 2:s 1 and s 2 Known,5.Determine whether to reject H0.,Because z=6.49 2.33,we reject H0.,Critical Value Approach,For a=.01,z.01=2.33,4.Determine the critical value and rejection rule.,Re

14、ject H0 if z 2.33,The sample evidence indicates the mean drivingdistance of Par,Inc.golf balls is greater than the meandriving distance of Rap,Ltd.golf balls.,Inferences About the Difference BetweenTwo Population Means:s 1 and s 2 Unknown,Interval Estimation of m 1 m 2Hypothesis Tests About m 1 m 2,

15、Interval Estimation of 1-2:s 1 and s 2 Unknown,When s 1 and s 2 are unknown,we will:,replace za/2 with ta/2.,use the sample standard deviations s1 and s2as estimates of s 1 and s 2,and,Where the degrees of freedom for ta/2 are:,Interval Estimation of 1-2:s 1 and s 2 Unknown,Interval Estimate,Example

16、:Specific Motors,Difference Between Two Population Means:s 1 and s 2 Unknown,Specific Motors of Detroithas developed a new automobileknown as the M car.24 M carsand 28 J cars(from Japan)were roadtested to compare miles-per-gallon(mpg)performance.The sample statistics are shown on the next slide.,Dif

17、ference Between Two Population Means:s 1 and s 2 Unknown,Example:Specific Motors,Sample Size,Sample Mean,Sample Std.Dev.,Sample#1M Cars,Sample#2J Cars,24 cars 28 cars,29.8 mpg 27.3 mpg,2.56 mpg 1.81 mpg,Difference Between Two Population Means:s 1 and s 2 Unknown,Let us develop a 90%confidenceinterva

18、l estimate of the differencebetween the mpg performances ofthe two models of automobile.,Example:Specific Motors,Point estimate of 1-2=,Point Estimate of m 1-m 2,where:1=mean miles-per-gallon for the population of M cars2=mean miles-per-gallon for the population of J cars,=29.8-27.3,=2.5 mpg,Interva

19、l Estimation of m 1-m 2:s 1 and s 2 Unknown,The degrees of freedom for ta/2 are:,With a/2=.05 and df=24,ta/2=1.711,Interval Estimation of m 1-m 2:s 1 and s 2 Unknown,We are 90%confident that the difference betweenthe miles-per-gallon performances of M cars and J carsis 1.431 to 3.569 mpg.,2.5+1.069

20、or 1.431 to 3.569 mpg,Hypothesis Tests About m 1-m 2:s 1 and s 2 Unknown,Hypotheses,Left-tailed,Right-tailed,Two-tailed,Test Statistic,Example:Specific Motors,Hypothesis Tests About m 1-m 2:s 1 and s 2 Unknown,Can we conclude,using a.05 level of significance,that themiles-per-gallon(mpg)performanceo

21、f M cars is greater than the miles-per-gallon performance of J cars?,H0:1-2 0,where:1=mean mpg for the population of M cars 2=mean mpg for the population of J cars,1.Develop the hypotheses.,p Value and Critical Value Approaches,Hypothesis Tests About m 1-m 2:s 1 and s 2 Unknown,2.Specify the level o

22、f significance.,3.Compute the value of the test statistic.,a=.05,p Value and Critical Value Approaches,Hypothesis Tests About m 1-m 2:s 1 and s 2 Unknown,Hypothesis Tests About m 1-m 2:s 1 and s 2 Unknown,p Value Approach,4.Compute the p value.,The degrees of freedom for ta are:,Because t=4.003 t.00

23、5=2.797,the pvalue.005.,5.Determine whether to reject H0.,We are at least 95%confident that the miles-per-gallon(mpg)performance of M cars is greater than the miles-per-gallon performance of J cars?.,p Value Approach,Because pvalue a=.05,we reject H0.,Hypothesis Tests About m 1-m 2:s 1 and s 2 Unkno

24、wn,4.Determine the critical value and rejection rule.,Critical Value Approach,Hypothesis Tests About m 1-m 2:s 1 and s 2 Unknown,For a=.05 and df=24,t.05=1.711,Reject H0 if t 1.711,5.Determine whether to reject H0.,Because 4.003 1.711,we reject H0.,We are at least 95%confident that the miles-per-gal

25、lon(mpg)performance of M cars is greater than the miles-per-gallon performance of J cars?.,With a matched-sample design each sampled item provides a pair of data values.,This design often leads to a smaller sampling error than the independent-sample design because variation between sampled items is

26、eliminated as a source of sampling error.,Inferences About the Difference BetweenTwo Population Means:Matched Samples,Example:Express Deliveries,Inferences About the Difference BetweenTwo Population Means:Matched Samples,A Chicago-based firm hasdocuments that must be quicklydistributed to district o

27、fficesthroughout the U.S.The firmmust decide between two deliveryservices,UPX(United Parcel Express)and INTEX(International Express),to transport its documents.,Example:Express Deliveries,Inferences About the Difference BetweenTwo Population Means:Matched Samples,In testing the delivery timesof the

28、two services,the firm senttwo reports to a random sampleof its district offices with onereport carried by UPX and theother report carried by INTEX.Do the data on thenext slide indicate a difference in mean deliverytimes for the two services?Use a.05 level ofsignificance.,3230191615181410 716,2524151

29、5131515 8 911,UPX,INTEX,Difference,District Office,SeattleLos AngelesBostonClevelandNew YorkHoustonAtlantaSt.LouisMilwaukeeDenver,Delivery Time(Hours),7 6 4 1 2 3-1 2-2 5,Inferences About the Difference BetweenTwo Population Means:Matched Samples,H0:d=0 Ha:d,Let d=the mean of the difference values f

30、or the two delivery services for the population of district offices,1.Develop the hypotheses.,Inferences About the Difference BetweenTwo Population Means:Matched Samples,p Value and Critical Value Approaches,2.Specify the level of significance.,a=.05,Inferences About the Difference BetweenTwo Popula

31、tion Means:Matched Samples,p Value and Critical Value Approaches,3.Compute the value of the test statistic.,5.Determine whether to reject H0.,We are at least 95%confident that there is a difference in mean delivery times for the two services?,4.Compute the p value.,For t=2.94 and df=9,the pvalue is

32、between.02 and.01.(This is a two-tailed test,so we double the upper-tail areas of.01 and.005.),Because pvalue a=.05,we reject H0.,Inferences About the Difference BetweenTwo Population Means:Matched Samples,p Value Approach,4.Determine the critical value and rejection rule.,Inferences About the Diffe

33、rence BetweenTwo Population Means:Matched Samples,Critical Value Approach,For a=.05 and df=9,t.025=2.262.,Reject H0 if t 2.262,5.Determine whether to reject H0.,Because t=2.94 2.262,we reject H0.,We are at least 95%confident that there is a difference in mean delivery times for the two services?,End of Chapter 10Part A,