Click to edit Master title style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,CHAPTER 9Estimation from Sample Data,to accompany,Introduction to Business Statistics,fourth edition,by Ronald M.Weiers,Presentation by Priscilla Chaffe-Stengel,Donald N.Stengel,2002 The Wadsworth Group,Chapter 9-Learning Objectives,Explain the difference between a point and an interval estimate.,Construct and interpret confidence intervals:,with a,z,for the population mean or proportion.,with a,t,for the population mean.,Determine appropriate sample size to achieve specified levels of accuracy and confidence.,2002 The Wadsworth Group,Chapter 9-Key Terms,Unbiased estimator,Point estimates,Interval estimates,Interval limits,Confidence coefficient,Confidence level,Accuracy,Degrees of freedom,(,df,),Maximum likely sampling error,2002 The Wadsworth Group,Unbiased Point Estimates,PopulationSample,ParameterStatistic Formula,Mean,Variance,s,2,Proportion,p,x,x,=,x,i,n,1,2,),(,2,2,n,x,i,x,s,s,=,p,p,=,x,successes,n,trials,2002 The Wadsworth Group,where =sample mean,ASSUMPTION:,s,=sample standard,Population,deviation,approximately,n,=sample size,normal and,t,=,t,-score for area,infinite,in tail=,a,/2,df,=,n,1,n,s,t,x,x,n,s,t,x,x,t,t,t,+,+,:,0,:,Confidence Interval:,s,Unknown,2002 The Wadsworth Group,Confidence Interval on,p,where,p,=sample proportion,ASSUMPTION:,n,=sample size,np,5,z,=standard normal score,n(,1,p),5,for area in tail=,a,/2,and population,infinite,n,n,z,z,z,0,:,p,p,z,p,p,p,p,z,p,p,),1,(,),1,(,:,+,+,2002 The Wadsworth Group,Converting Confidence Intervals to Accommodate a Finite Population,Mean:,or,Proportion:,2002 The Wadsworth Group,Sample Size Determination for from an Infinite Population,Mean:,Note,s,is known and,e,the bound within which you want to estimate,is given.,The interval half-width is,e,also called the maximum likely error:,Solving for,n,we find:,2,2,2,e,z,n,n,z,e,s,s,=,=,2002 The Wadsworth Group,Sample Size Determination for from a Finite Population,Mean:,Note,s,is known and,e,the bound within which you want to estimate,is given.,where,n,=required sample size,N,=population size,z,=,z,-score for(1,a,)%confidence,2002 The Wadsworth Group,Sample Size Determination for,p,from a Finite Population,Mean:,Note,e,the bound within which you want to estimate,is given.,where,n,=required sample size,N,=population size,z,=,z,-score for(1,a,)%confidence,p,=sample estimator of,p,n,=,p,(,1,p,),e,2,z,2,+,p,(,1,p,),N,2002 The Wadsworth Group,A Confidence Interval Example,cont.,Since,s,is not known but the population is approximately normally distributed,we will use the,t,-distribution to construct the 90%confidence interval on the mean.,n,s,t,x,x,n,s,t,x,x,t,t,t,+,+,:,0,:,),621,.,64,179,.,51,(,721,.,6,9,.,57,20,384,.,17,729,.,1,9,.,57,729,.,1,So,05,.,0,2,/,19,1,20,384,.,17,9,.,57,=,=,=,=,=,=,n,s,t,x,t,df,s,x,a,2002 The Wadsworth Group,A Confidence Interval Example,cont.,Interpretation:,90%of the time that samples of 20 cars are randomly selected from this agencys rental cars,the average mileage will fall between 51.179 miles and 64.621 miles.,2002 The Wadsworth Group,A Sample Size Example,cont.,From the problem we learn:,(1,a,)=0.95,so,a,=0.05 and,a,/2=0.025,e,=0.03,Since no estimate for,p,is given,we will use 0.5 because that creates the largest standard error.,To preserve the minimum confidence,the candidate should sample,n,=1,068 voters.,1,.,067,1,2,),03,.,0,(,),5,.,0,)(,5,.,0,(,2,96,.,1,2,),1,)(,(,2,=,=,=,e,p,p,z,n,2002 The Wadsworth Group,