Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc. Chap -!"ne- an# $%o-Sa&ple Esti&ation Pro'le&s(Confi#ence Inter)al*Chapter 9+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -2Chapter 0oalsAfter completing this chapter, you should be able to: 1isting/ish 'et%een a point esti&ate an# a confi#ence inter)al esti&ateConstr/ct an# interpret a confi#ence inter)al esti&ate for a single an# t%o pop/lation &ean /sing 'oth the 2 an# t #istri'/tions3or& an# interpret a confi#ence inter)al esti&ate for a single an# t%o pop/lation proportion an# )ariances1eter&ine the re4/ire# sa&ple si5e to esti&ate a &ean or proportion %ithin a specifie# &argin of error+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -6"ne- an# $%o-sa&ple Eti&ationContent: Confi#ence Inter)alsSingle Sa&ple7 Esti&ating Pop/lation Mean, $olerance 8i&its$%o Sa&ple7 Esti&ating 1ifference t%o &eansPaire# "'ser)ationsConfi#ence Inter)als for the Proportion, p Confi#ence Inter)als for the 9ariance, 2 1eter&ining the :e4/ire# Sa&ple Si5e+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -4Point an# Inter)al Esti&ates; point esti&ate is a single n/&'er, a confi#ence inter)al pro)i#es a##itional infor&ation a'o/t )aria'ilit,Point EstimateLower Confidence LimitUpperConfidence LimitWidth of confidence interal+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap - ?9ariance @2S2+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -AConfi#ence Inter)alsHo% &/ch /ncertaint, is associate# %ith a point esti&ate of a pop/lation para&eterB;n inter)al esti&ate pro)i#es &ore infor&ation a'o/t a pop/lation characteristic than #oes a point esti&ateS/ch inter)al esti&ates are calle# confi#ence inter)als+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -CConfi#ence Inter)al Esti&ate;n inter)al gi)es a range of )al/es7$aDes into consi#eration )ariation in sa&ple statistics fro& sa&ple to sa&pleEase# on o'ser)ation fro& ! sa&ple0i)es infor&ation a'o/t closeness to /nDno%n pop/lation para&etersState# in ter&s of le)el of confi#enceCan ne)er 'e !00F confi#ent+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -.Esti&ation Process!mean, ", is un#nown$Pop/lation:an#o& Sa&ple%ean & ' ()*ample+ am 9(, confident that " is between -) . /)0+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -0eneral 3or&/la$he general for&/la for all confi#ence inter)als is7Point Estimate ' !Critical 1alue$2!*tandard Error$nErrorStandard =+here+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -!0Confi#ence 8e)elConfi#ence 8e)elConfi#ence in %hich the inter)al %ill contain the /nDno%n pop/lation para&eter; percentage (less than !00F*+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -!!Confi#ence 8e)el, (!-*S/ppose confi#ence le)el G xx!x2K2 K2 !+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -!CExa&ple; sa&ple of !! circ/its fro& a large nor&al pop/lation has a &ean resistance of 2.20 oh&s.+e Dno% fro& past testing that the pop/lation stan#ar# #e)iation is .6< oh&s.1eter&ine a en@2 e =Sa&pling error (&argin of error*+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -421eter&ining Sa&ple Si5een@2 e =(continued)22 2eZn =Ho% sol)e fornto get+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -461eter&ining Sa&ple Si5e$o #eter&ine the re4/ire# sa&ple si5e for the &ean, ,o/ &/st Dno%7$he #esire# le)el of confi#ence (! - *, %hich #eter&ines the critical 2 )al/e$he accepta'le sa&pling error (&argin of error*, e$he stan#ar# #e)iation, @(continued)+alpole,Pro'a'ilit, an# Statistics for Engineers - Scientists, .th e., Pearson E#/. Chap -44:e4/ire# Sa&ple Si5e Exa&pleIf G 4