Week 6 Math 225n Statistics Quiz, Quizzes of Mathematics

Download Week 6 Math 225n Statistics Quiz and more Quizzes Mathematics in PDF only on Docsity! Week i6 iQuiz Question i1 A istatistics iprofessor irecently igraded ifinal iexams ifor istudents iin iher iintroductory istatistics icourse. iIn ia ireview iof iher igrading, ishe ifound ithe imean iscore iout iof i100 ipoints iwas ia ix¯=77, iwith ia imargin iof ierror iof i10. Construct ia iconfidence iinterval ifor ithe imean iscore i(out iof i100 ipoints) ion ithe ifinal iexam. Answer: i (67, i87) Question i2 A irandom isample iof iadults iwere iasked iwhether ithey iprefer ireading ian ie-book iover ia iprinted ibook. iThe isurvey i resulted i in i a i sample i proportion i of i p′=0.14, i with i a i sampling i standard i deviation iof iσp′=0.02, i who preferred ireading ian ie-book. Use ithe iempirical irule ito iconstruct ia i95% iconfidence iinterval ifor ithe itrue iproportion iof iadults iwho iprefer ie- ibooks. Question i3 The ipages iper ibook iin ia ilibrary iare inormally idistributed iwith ian iunknown ipopulation imean. iA irandom isample iof ibooks iis itaken iand iresults iin ia i95% iconfidence iinterval iof i(237,293) ipages. What i is ithe icorrect i interpretation iof ithe i95% iconfidence i interval? We iestimate iwith i95% iconfidence ithat ithe isample imean i s ibetween i237 iand i293 ipages. We iestimate ithat i95% iof ithe itime ia ibook i s iselected, ithere iwill ibe ibetween i237 iand i293 ipages. iWe iestimate iwith i95% iconfidence ithat ithe itrue ipopulation imean i s ibetween i237 iand i293 ipages. Question i4 That iis icorrect! That iis icorrect! Answer: i( i0.10, i0.18) That iis icorrect! The ipopulation istandard ideviation ifor ithe iheights iof idogs, iin iinches, iin ia icity iis i3.7 iinches. iIf iwe iwant ito ibe i95% iconfident ithat ithe isample imean iis iwithin i2 i nches iof ithe itrue ipopulation imean, iwhat iis ithe minimum isample isize ithat ican ibe itaken? iRound iup ito ithe inearest iinteger. Answer: i 14 idog iheights Question i5 Clarence iwants ito iestimate ithe ipercentage iof istudents iwho ilive imore ithan ithree imiles ifrom ithe ischool. iHe iwants ito icreate ia i98% iconfidence iinterval iwhich ihas ian ierror ibound iof iat imost i4%. iHow imany istudents ishould ibe ipolled ito icreate ithe iconfidence i nterval? z0.10 i i z0.05 i i z0.02 5 z0.01 iz0.005 1.28 1.64 1.96 2.32 2.57 i 2 5 0 6 6 Use ithe itable iof ivalues iabove. Question i6 The iaverage iscore iof ia irandom isample iof i87 isenior ibusiness imajors iat ia iuniversity iwho itook ia icertain istandardized itest ifollows ia inormal idistribution iwith ia istandard ideviation iof i28. iUse iExcel ito idetermine a i90% iconfidence iinterval ifor ithe imean iof ithe ipopulation. iRound iyour ianswers ito itwo idecimal iplaces iand iuse iascending iorder.. i Score 516 536 462 461 519 i 496 517 488 521 HelpCopy ito iClipboardDownload iCSV Answer: i (509.30, i519.18) That iis icorrect! That iis icorrect! Answer: i 846 iStudents That iis icorrect! Question i12 The igraph ibelow ishows ithe igraphs iof iseveral inormal idistributions, ilabeled iA, iB, iand iC, ion ithe isame iaxis. iDetermine iwhich inormal idistribution ihas ithe ismallest istandard ideviation. A iB iC Question i13 The iresistance iof ia istrain igauge iis inormally idistributed iwith ia imean iof i100 iohms iand ia istandard ideviation iof i0.3 iohms. iTo imeet ithe ispecification, ithe iresistance imust ibe iwithin ithe irange i100±0.7 iohms. iWhat proportion iof igauges iis iacceptable? • Round iyour ianswer ito ifour idecimal iplaces. Question i14 A ibaker iknows ithat ithe idaily idemand ifor istrawberry ipies iis ia irandom ivariable ithat ifollows ithe inormal idistribution iwith ia imean iof i31.8 ipies iand ia istandard ideviation iof i4.5 ipies. iFind ithe idemand ithat ihas ian i8% iprobability iof ibeing iexceeded. • Use iExcel, iand iround iyour ianswer ito itwo idecimal iplaces. That iis icorrect! That iis icorrect! Answer: i 0.9804 Question i15 A igroup iof ifriends ihas igotten ivery icompetitive iwith itheir iboard igame inights. iThey ihave ifound ithat ioverall, ithey ieach ihave iwon ian iaverage iof i18 igames, iwith ia ipopulation istandard ideviation iof i6 igames. iIf ia isample iof ionly i2 ifriends iis iselected iat irandom ifrom ithe igroup, iselect ithe iexpected imean iand ithe istandard ideviation of ithe isampling idistribution ifrom ithe ioptions ibelow. iRemember ito iround ito ithe inearest iwhole inumber. σx¯=6 igames σx¯=3 igames σx¯=4 igames μx¯=18 igames μx¯=3 igames μx¯=9 igames • Question i16 • An ielementary ischool ihas ia ipopulation iof i635 istudents, i600 iof iwhom ihave ireceived ithe ichicken ipox ivaccine. iThe ischool inurse iwants ito imake isure ithat ithe ischool imeets iall istate irequirements ifor ivaccinations iat ipublic ischools. • Find ithe ipopulation iproportion, ias iwell ias ithe imean iand istandard ideviation iof ithe isampling idistribution ifor isamples iof isize in=120. Answer: i 38.12 That iis icorrect! That iis icorrect! • Round iall ianswers ito i3 idecimal iplaces. • p i= i0.945 • μp̂ i= i0.945 • σp ̂ i= i0.021 Question i17 The ilengths iof itext imessages iare inormally idistributed iwith ian iunknown ipopulation imean. iA irandom isample iof itext imessages i s itaken iand iresults i n ia i95% i confidence i nterval of i (23,47) icharacters. What i s ithe icorrect i nterpretation iof ithe i95% iconfidence i nterval? We iestimate iwith i95% iconfidence ithat ithe itrue ipopulation imean iis ibetween i 23 iand i47 icharacters. iWe iestimate iwith i95% iconfidence ithat ithe isample imean i s ibetween i23 iand i47 icharacters. Question i18 Given ithe iplot iof inormal idistributions iA iand iB ibelow, iwhich iof ithe ifollowing istatements iis itrue? iSelect iall icorrect ianswers. • • That iis icorrect! • We iestimate ithat i95% iof itext imessages ihave ilengths ibetween i23 iand i47 icharacters. That iis icorrect! Answer: i (894.43, i940.21) Question i22 Hugo iaverages i40 iwords iper iminute ion ia ityping itest iwith ia istandard ideviation iof i15 iwords iper iminute. iSuppose iHugo's iwords iper iminute ion ia ityping itest iare inormally idistributed. iLet iX= ithe inumber iof iwords iper iminute ion ia ityping itest. iThen, iX∼N(40,15). Suppose iHugo itypes i56 iwords iper iminute iin ia ityping itest ion iWednesday. iThe iz-score iwhen ix=56 i s i . iThis iz-score itells iyou ithat ix=56 i s standard ideviations ito ithe (right/left) iof ithe imean, . Correctly ifill iin ithe iblanks iin ithe istatement iabove. Suppose iHugo itypes i56 iwords iper iminute iin ia ityping itest ion iWednesday. iThe iz-score when ix=56 iis i−0.889. iThis iz-score itells iyou ithat ix=56 iis i0.889 istandard ideviations ito ithe ileft iof ithe imean, i40. Suppose iHugo itypes i56 iwords iper iminute iin ia ityping itest ion iWednesday. iThe iz-score when ix=56 iis i−1.067. iThis iz-score itells iyou ithat ix=56 iis i1.067 istandard ideviations ito ithe ileft iof ithe imean, i40. Suppose iHugo itypes i56 iwords iper iminute iin ia ityping itest ion iWednesday. iThe iz-score when ix=56 iis i1.067. iThis iz-score itells iyou ithat ix=56 iis i1.067 istandard ideviations ito ithe iright iof ithe imean, i40. Suppose iHugo itypes i56 iwords iper iminute iin ia ityping itest ion iWednesday. iThe iz-score when ix=56 iis i0.889. iThis iz-score itells iyou ithat ix=56 iis i0.889 istandard ideviations ito ithe iright iof ithe imean, i40. Question i23 Hugo iaverages i62 iwords iper iminute ion ia ityping itest iwith ia istandard ideviation iof i8 iwords iper iminute. iSuppose iHugo's iwords iper iminute ion ia ityping itest iare inormally idistributed. iLet iX= ithe inumber iof iwords iper iminute ion ia ityping itest. iThen, iX∼N(62,8). Suppose iHugo itypes i56 iwords iper iminute iin ia ityping itest ion iWednesday. iThe iz-score iwhen ix=56 i s i . iThis iz-score itells iyou ithat ix=56 i s standard ideviations ito ithe (right/left) iof ithe imean, . Correctly ifill iin ithe iblanks iin ithe istatement iabove. That iis icorrect! That iis icorrect! Suppose iHugo itypes i56 iwords iper iminute iin ia ityping itest ion iWednesday. iThe iz-score when ix=56 iis i0.75. iThis iz-score itells iyou ithat ix=56 iis i0.75 istandard ideviations ito ithe iright iof ithe imean, i62. Suppose iHugo itypes i56 iwords iper iminute iin ia ityping itest ion iWednesday. iThe iz-score when ix=56 iis i−0.75. iThis iz-score itells iyou ithat ix=56 iis i0.75 istandard ideviations ito ithe ileft iof ithe imean, i62. Suppose iHugo itypes i56 iwords iper iminute iin ia ityping itest ion iWednesday. iThe iz-score when ix=56 iis i0.545. iThis iz-score itells iyou ithat ix=56 iis i0.545 istandard ideviations ito ithe iright iof ithe imean, i62. Suppose iHugo itypes i56 iwords iper iminute iin ia ityping itest ion iWednesday. iThe iz-score when ix=56 iis i−0.545. iThis iz-score itells iyou ithat ix=56 iis i0.545 istandard ideviations ito ithe ileft iof ithe imean, i62. Question i24 Lisa ihas icollected idata ito ifind ithat ithe inumber iof ipages iper ibook ion ia ibook ishelf ihas ia inormal idistribution. iWhat iis ithe iprobability ithat ia irandomly iselected ibook ihas ifewer ithan i168 ipages iif ithe imean iis i190 ipages iand ithe istandard ideviation iis i22 ipages? iUse ithe iempirical irule.Enter iyour ianswer ias ia ipercent irounded ito two idecimal iplaces iif inecessary. Question i25 Lisa ihas icollected idata ito ifind ithat ithe inumber iof ipages iper ibook ion ia ibook ishelf ihas ia inormal idistribution. iWhat iis ithe iprobability ithat ia irandomly iselected ibook ihas ifewer ithan i140 ipages iif ithe imean iis i190 ipages iand ithe istandard ideviation iis i25 ipages? iUse ithe iempirical irule.Enter iyour ianswer ias ia ipercent irounded ito two idecimal iplaces iif inecessary. That iis icorrect! Correct ianswers: i2.5% That iis icorrect! That iis icorrect! Answer: i 15.87%