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by: Aileen Davis

ElementaryStatistics MATH0013

Marketplace > Sierra College > Mathematics (M) > MATH0013 > ElementaryStatistics
Aileen Davis

GPA 3.77


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Class Notes
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This 40 page Class Notes was uploaded by Aileen Davis on Tuesday October 20, 2015. The Class Notes belongs to MATH0013 at Sierra College taught by JamesSullivan in Fall. Since its upload, it has received 24 views. For similar materials see /class/225375/math0013-sierra-college in Mathematics (M) at Sierra College.

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Date Created: 10/20/15
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ggntmte tqpage 122 rest is79 par 7 minu re is valid bbptbm Example 0 9 s r atls rlcs s ruden r 39rrandomlly so 39 selec red 16 new Textbooks in The 9ege books rorer heresu Ifrsofher39 sa mp ega ve r a mean39Dr39ice of 7041 ahda s randar ddevi39a rion of 1970 Question hecollege cafalt s ra re s fhat D theaverage39priceiofm jexfbookAaf The booksmr 7 7 less Than 75 Based on The s r39uden5f39s sample V is thisstafmf J si ri fied PValue Solution V H01i Z4975 quot Cl9imijsquotnoi39 7 H 1 Ltltr745 laim sjus ra39 ei Let a 3 o c YTeEtn t m T P l a a IA E1195 t 9319796954 xB41 51838536413 5x197 xa41 n Sx19 7 u un gtun n16 C JQU19 9 Draw fSi nEE TlT pivalue 2 1813quotgt 5 7 we fail To rejec r H09 OEOL Answer Since we fail To rejecT H9 There s i n suffi39c i nT sa miple e Vidente l39O subsfdhl39iii l39 l h claim ih The Elle f lt ih r rhe mean priee of a Tex rbook a r This 666666 66 r 66 I l l u o do 4 7 colleqe is less quotthan 75 ThmeTle imimd i 39 fhe catalog isrno r comple rely ius rified Requirement Check he sample damweb obtained 9amp0 resul r of a simpler random sample 7 inicefrhe sample size is nio39r 39 4 39suffici ently1a 6quot39U E1 fs30 1he popula rion mus r e normally J A I UISIHULIICU 39incejhiscannotbeconf irmed with 39 The da ra provided we must assume i IhaLthe prjee QfJextbonsaLihe 7 bookstore is normally disTribuTed ChiSquare X2 Tes139 39 ChiSquare hypothesis Test is l 139 used To compare abserved T frequencyvgtdisfrribu riens 39 Sample da r a To distributions 7 weegtltp2ctedtoobserve according Tossome Idea fr WPT trmiz edW lu sl 6be ChiSquare X2 Tes139 WTe s r iwito rswif T he i39d39ea39wa5i a gaodiiflfo rno r7 O C O 2 4G 4 2 yo 445 o o r ha s wewah r393rio determine if39theexpierc redvaIues 7 V reasonably ma rch in f rhe Bb ser39vedW lues 6613M X2 600d ness of PHquot T251 HOTThe i de usai 11W rheexpec redmauesisvaLd fag izri r bbb bmbbl bbebmbn o H1 The quotideaquot used To generate The expec red values Is no r WlidT Ea diii 39 X2 Goodness ofFi39rquot Tes139 e r 0c 7 level of significancequot 9 Zes f Statistic Formula Q 7Oi are 139heobser ved values dam Ei areThe expected values E no and k is The number of categories c X2 Goodness ofFi39rquot Tes139 Enter The observed values in n rer39quothe expecfredwalueS in39IJ v Y2GOF ENTERT ENTERT f pval39ue s on rej ec r Ho 1f pvalue gt 0L fqil rorej ec ro f X2 Goodness ofFi39rquot Test 70 f you rejec r HoT r he ideaquotquot if rusedifogeneratg rhe expee redi values39js noLvalidI rwasai r bad quot f y39OU F e j eC39T Ho T h ideaquot usedJMemmtei xpe c red values is valid If i was a good fi rquot bop tbmbbqbcbo Example 6 Before my students completed examiy iiTnSTI pred39iETd t 1th 30 of my students 7 quot would earn an 40 a Bquot 2 0quotoai C 10EJ BW39F39 i estheaceuraeyof my4 739 39pJgdicTjQnsusinzg31x 1 goodnessof fi f res r bb Solution HfMy plTed i c re dee fdis rr39ib u rion per39cen ragesartef39 Ei quotpi Expecfed 624 156020 7 312 15630310 156 156100 156 Calculations L2 L3 3 PPQNXEEDF m 4 2 x2 5s AP I 4 L3H DF 5848298598 1192298786 3 Done 5 Irince the pgvaluew 39o119gto05 Ea7 7 we fail toire ieet39l lo Conclusion hmmtedfmdicted D val uesreasonaby39mat39c hintquot Eih 9b gcyegiglu 7 Hengemy ptladlctedgta e 5 distribution percentages for my statistics students were accurate Example Elk Tied ValoW39 7 7 75Wi39l I39 bitk BIU 5 39331 i i k7 iifi i3 mup39mk e awi39 be heir favor i re primaryg I O LVN 3 bbbbb Question I bbbbbbbon a s our pr39edlc red percentages f i b I53 ideb r iT T F d 3967 coor39s accura re Aeaner39e39d rocon ductagX3 goodness offi r Tes r TO i answer THE queSTIEL bb bba X2 600d ness of PHquot T251 1 Owlw ed iETe d39per cen rages f orpeop esfavori retpr39imar39y 7coorsrareraccurafe r H0 H1 OUr pr di cfed per n rag 39for39peopesfavoriteprii many colors are nof accurate 7 e39Loc 35 e do 4 i9 1 o r a 40 2 0 13 G o u 70 40 Calculations Conclusion Example andom lye pick 7a number from 1 g 1 1 0 4 ha hnn39 u u ih eiaked oso7dowpeopr 39pickvnumbers fromliro 4 1 r39andomy Solution 3 ickin gfaT39r39and om wouldim ean rhategghnumberimdjhe 5392 samerchanee of being cl selecTed 39 t 1 hus pZ0252590 39 oreachof rhefour39numbers bb bba X2 600d ness of PHquot T251 39 z39PmaIeEi ckmtwsifm 1 to4 rando m39ly wehenas kedto I o H1 39Peo l do fp i k number s 39from1to4randomywhen asked ro do so e39Loc 35 505mm 515mm Calculations Conclusion Hypothesis Testing 91 if you or39 someonecaimsrtor 39 know the value of a particular 10 i population pargrneg rerryqu can quot test your39 ror39 tliheir39 claim by i 7 using hypothesis testing 1 techniques Example think that 20 of siW fGol39Iegequotstatisticsstudent539 gt attendischool parttimeT 650606be b m Usemour students su rveydata iq and a 5 level of significance tot s t my clc r x c to 43 7 o 6 bba Solution fthe 44 students in our fS39urveyTS39or eienmIledfin fewer than 712unigts r PValue Method l I F OPLIESL IESL PD2 2 39 8 1 1344 x n44 PPD Pu gtPn Calcu ate Draw Tests Involving Proportions Mer rqm requlremen rs 39mu T39 be 0 fsa r i sf39ied or der toj r39ify fhi39s r I39e s l39i39hg FOC dUFezr he sample data mus r b e obTained a so nequLota simplerando m r sam ple397andh sample size must be sm IICVlel39II IY large WeconsideP The39somgleTo be sufficien rlyilame whenever np 9 and mum 3 Example Do more than TwoThirds of 2 iA mergansifavor39wggnpgign 7 70 e fmancerefor m r o a under To answerthi 5 questigiw operlyi we mus r 39 conduc r a hyp39o rhesjsTes r quot procedur39e Example 7 USBTThBT39FOJ lowingsump e data iwi rrhr 0c O01 ro conducv ri rhei Vlccor39ding roa CNN poll oy riof flol5 A me cans sunvey d39 z favoredicampaign finance reform Lfet QQl 3 1PPOPZTESt 1PPDPZTESL i MHZ3 i ProPgt66667 r x 2 z6 3423691 39 7 n P189531 18 quot 7 PraPPn Pu I5 762591133 n 39 Calculate Draw n1815 r f3i nc ethe piv39a39lue 20000 51001 0c we reject Ho Answer 390 i D quotMorejhan39fwoa rhirdsrof Americansifavor campaign finance reform 5In fac r This propor rion i appears to be abou r Three out of four Example Basedon a nafr i ona pol US39A Today poried ihai 42 ofi z 7iridividualsifelttheymere 390 worse off Than one year ago politician feels Tha r this 39 figureisi roohighfor her E dis Trie rfSOrs39he rcommissi39ons h er ownsurvey Example 9 his Survey found That 3814 V of The 250 randomly selected ciy r iiens iniher39 d39i39sTric tfelt theywer39eworse of f rhanone CD 7 lt rlt3 3 ltD Ym90 1 co 0705 is The politician39s 9 is rion emf her39 diE rF39iEf cor39r39ec r PValue Solution 39LI M70 um 4 I I 0391quot quot 0 198 1939 9915Iy11 meE p lt 42 39 VasT g tareT0041 h u D quot L t b t 005 1 PF OFZTESt 1PPDPZTesL 39 P 39 39 n42 PPOP gt696 z39115327617 n25 P124398288 PPOP PII gtPn 93 39 Calculate raw 7 n258 x 250038496quot I Tefpivaltre a 01 24fgtf005Toc 39 we fail To rejec r H01 Answer 9 iTrher39eWIs no r enough sample evi39den ce TOiclear39 Iy s ra retr ha r 9 thepolLthjanisqssediam abou r hend isn rli39c r iscorr39ee r i X2 Test for Independence ne specific application of frhe i x gOOdHessoffi1 6er lo involves Testing g 7 a55ump rion That two events E7 ar39eindependentoteacbother l Tha r S1390 de rer mme If rwo par Ticuiar variabies have no 39 affecton each other Independen39l39 Even39l39s wefevenfrsE andF are inderpenden rfif L YE gm F53 P753 abbbbi c act do 4 2 74 do 0 r 39 hexzwgoodness39offi r res r i use these pmbabi liiies to 7 rest for39 independence ihbb bba X2 Test for Independence I o z The variable quot in queSIion ar eindependenfr 56 7Srm i i 519116 varia aiiaqge iion gt quot7 independent i39 aaaan bbb tbmbb39fibbcb X2 Test for Independence gt c39 at 0c level of Significance39 0 esT39S ra ris ric Formula 39 6 O Ezr 72 239rr gt1 gt1 7 I J Ofdrethe abservedivaInes 39 Eii ar39e39fhe expected VCIILIGS39 Q r39 is139he numbewof categories for The39finsf r var39iabekand c is Thernumber aficategonies for39 The second variable X2 Test for Independence EYWTEd Va ILEs y ni 711 7 r 7 column total grand total ting calc gj cdlcula Feg ihese OJILiESf EQI US39 X2 Test for Independence n39ihg 1183pr cglculmortenterthg QbsemedMaluesin romaTIjx A byi pressing 5quot MATRX gtgtEDIT LENTEE quot 7 M4TR1XA r xc 039 039 039 521 022 02 7 70m Onz 6r7 7 X2 Test for Independence V hen calculate the results by pressing STAT 39FVTES TS J TEFX Z Tat T MMHENTERHENTERJ r fpN39ulue Kfail to reject Ho Xz Test for Independence 1quot were 39 eat Haithen we econclu erthattheitwo variables arergnot independent if each other 39 h39is means that thesevariables V d oraffectieachrrotherandare 1 related or depend on each NW X2 Test for Independence 1 f we quotfai Itareject Ho then 7 we if iconcludethatt heftWO variablesareindependeniofi Whether 39 h39is means that these variables do not affect each other and 397 are not related or don39t iTziepend on eachTJt39W Example afa dom sampIe of politically39and39whefher they th39ought fhe39effects Of Solution fques onrisiindepgnden riof rheirir 397 39ponthnl identifico rion Solution 0 39ME39S MFiTH ram F ace Test a gig absawed Fl 39 ExPEGLEd B HTRIXEF 2 6 Calculate Draw 5 31 7 T DFILC Egg XzTest SaMPTIn XZS15722268 PrOPZInL 51 185984r19 7 into pvalue 0000s 005211 we reject Ho Answer I l n Amemcan39s response frowns QUES B isi fii d d 39 f i t hiei eroJ it i ca iden ri ca r ion Comments h q r isth qn A mge r39icgn responded39to 1h isequesfion dependedontheir pOIITIcal Iucmll ILUI Ian 7 e observed fewer republi39cansihan 39 was expected Tha r Thouqh r The effects of global warming have begun e observed more democra rs than was j gpec red fha r mough r The effec rs off global warming have begun Example fbllowing Male Female 5 gendeT is dependeif dtiSe SoluTion Ho A person39s gender is o independenT of The Type of 5 vehicle They drive Er person39s qendyimTi39 L fi39 dmiai o Wiy p of 0 vehicle They drive et a 0 na SoluTion C j MES MFiTH39Q Ii 3124951 EEi EET awe e TRIHIH 24 Calculate Draw 55 as 110 so 2395 DIT CFILC Biz Test T2 SaMPTIr39I R21324318245 1 ProPZInt aa41391624 2ProPZInt dr3 EMFTest ince pvalue u 0004 005a we rejecT Ho Answer ru 1 T appearsT haTa39pers onquot39si igenderri39s inoT independenTioffr do The vehicle They drive a so drIv quot depequot s 397hereforeThetypeiof vehicle 7 NW N 1 e d i somehow on TiEirT39gerer Question Does The Type of degree earned r In The Um red S rggjres quotlgsj year t a pearto be indep idg i of ege iwer of The degree J39 I CbIPICIII x0 fes shouldbeused for 1 TesTforindeperndtence Sample Do39l39o di39gplay39sthe counts in Female Male Solution 39 H5 T hey rype of degreefeorned39 in theiln i tedyStates IasLyeare is 7 fm j e p mjewmf f he gewder o f39f he degree reCIpIenT 34 Hp The rype of degree earned in 0 I The UnITedSTaTesrlasT yearls no i independent of The gender ofquot rhe 39 degree recipient Solution gt1 1 6139 I 005 39TESL 39FI TR I X39I39H39J 273 Ubsewem H 39 EXPacted B E 2 Calculate Draw I EHLC XE Tegt fggggggmt 39 Xi4814113866 2 PmP21ntZI 39535343335932 xz Te L 1 in e pVQIue r 9134 gt 905 g mail TWJECT Ho Answer heiryperof degree earned 5 The39Un i re disiafesiIas riyedr T doe sappeartobe 7 39 i pfen d f of rhegender of 7 Thedegree r39ec i r Question E1 on our39 STU de nT survey ju datacanoneconcludejhata 5 r rudenfrsrmfinqrofi rhejrimafhi 390 ability is made independent of J their gender X2 Test for Independence Ho A studen r39fs r a ringrof Their 4039 ma rh abili ry is made i independen riof Their39gender 77 Fir A s ruden r39s r39a rinq of Their Wimbilityfisnotmdf 0 independenT Of Thei r gender 61 m L 0 na S39l39uden39l39 Survey Data QOS Math Ability Rating Beiow dual Above 45 Solution 3 FINES NFITH39 3 ill H1 2x3 3 2 I Calculate Draw s 15 1 11 I 1 DIT DFILC age Test 39 T2 53NPTIFI X21551762 1 PF OPZII 1L P 4157 3423E 39 PPDPZInt F2 ZTestm 7 ince pvalue 0416 00491 we f ai 70 reject Ho Answer 39 es i used Tn our sample one could iconciudefrha39ria stud nis r 739 nafing mf h eirmathrabinli ryjs made independen r of Their gender Comment H bbon obbbb Tr p earis T hat r hWi n which a sTudenT rq reSquotTheir39 0 mgthvqbiiigtd9 senoid MEL 7 on jrheir39 gender hatis Therdis rrlibur rion of 70 maTVhLabrilityira rings werie N simjlan f or39 mqlesangd females bah Inferential Statistics We use sample results to i0 draw an inference reacha conclusion makeastatement 1 aboutthe entire population 7 Where aneVIi39wo basir i39ypes of i ferent idist tis tics pro b i quot9 Mypmt for 7apartieuar7popuIation 7 quotQ parameter you can estimate it V us39ing confidence inter val 39 techniques c 5 hatrisrweareinterestediin making an estimate U Wdi tion Wforecast Confidence Intervals Tn dence intervals have a u hjg hiprobabiityof g surrounding the actual O the form uSample M gingf Estimate Error 39 Confidence Intervals 37L7lt ac rual valuez R V 1 a 39 I A r 3 ha r iswe es r ima rey rheacfual 7 7 populatiionvaluetobewirthin 7 our In rervqlLfr39om L To R wu rh 17d39confidence 666M Confidence Level 1Ql iS calledThe confidence Java r WEis39jrh e probabili fy Tha r 1W interivqlrmake39s a correct eegtjmgig he standard is 95 39 where on 5 wbmm 6613M Significance Level isquotca ed quotrhefsign izf iicance level bbb tbmiybl bbbbbobob his i s rrh e priobabi Ii ryjrha rihe 7 in rervalaoes no r make a 1 correct es ri r d r e hieygwisgL sad E 534 L39mie ss gmrfed mh rwis ei Confidence Interval for p 1P7rgpZIriu here The samplesize39n is39suf39ficien rly large n gt 30 z is found in Table A2 trom we and A x he sarerle propor on p I l V For The TI 83 Calcula39l39or ic o cal c ulcT re a conf39i dence f intenvaljonmpopulaTion 7 igproporfionrpTpre ss S STAT Tagsls 039 397 5 Azi ropZIn r Eh ler ob bba Example 1 1 1 mail lama cl demw HST wee kf l3i8 ou l39of139025 Am ri gn 599 gd 19ugh rbgt The news media was Too liberal h Elam weigh5551 lbb or and The aallup poll resul rs To 2 t estimate rhejqctual propor r39ion of Americans Tha r f Thlhk th hQWS f leCl lS 0077 quot Iibera 9 Express youranswer 39 sxmbglicgJJyqndLerbqJyf 0 1 Pr o ni 7 l rop ini 38 3933456 n 1825 42731832 CLeuel 95 n1E125 Calculate 0397 ltp lt0458 Answer H so go ymbgltmlly 397 o lt p lt 458 o 3 man J j Lesf i r n redihd r befween 39730 T and 43958 o of Americans rhin39k rha r The news media Is Too i39l iberai Comment quot iconfid ntiyiconciudeWThaT r A mericans ho h in kt hatth e news media is 00 liberal are in The minori ry Example c os r semasfrer The A Cisfud nfr 392 ngte com missionedngEY Where 7357 Sierra Collegers ruden rs were 7 randomly seIee red In resEonse Toe rhe quesiW 7re ou a To acco I useri 58 res on edWi fhlyesi 39 T rrue percenfage of S ierra C6e9e siud en fs Thaf39use39robacca ixpress your answersymbBI iazlly d I gverlnnlkl quotIT 83 Solution IST39A TTFVTESTS v b ATIZPWZIinTT Enter 1 Pr0PZInL rrl PPDPZII I L gt658 ii 131335 19453 n35 162464986 CLeuel S n357 Calculat 39 39 0130ltplt0195 Answer igsmboumny 130 lt7 p lt 195 OV FE vlly 0 is esfim MTTW9Ocp T fld hf ll i t lif TW m r 130 candi195 of5ierma T College s ruden rs use Tobacco Comment in ge Theiconjfidenge39inter39ml fan 3910 ml up L 1 u E L3 is complei rielyh elow 27 which is The 0 Wtage oprczplf rl 39r use I Tobacco ri39n rl le generalpopula rionxwwe canrrcenfiden rly conclude lha r Sierra 2 College s ruden rs use Tobacco of a j lower r a re Thanipeorple in Thegener al populatipn Z gsiulispp g hgugh mj i Qw ng 2 692 9Lr r shouldbemade illegal r J 7 llul IVIIVVIUO Question lt9 4 Usether39es39ultsofquottheUSA Today 07 polllkto estimate the proportion of 4c i adaligihat thian gambling on college sports should be made j IllegalinationWIde 3 xpr ess your L answen symbo l ieal39ly and verbally iST39ATrFrTES T s g n 501 vix 39OAEZQTjO 244989 5 Wm ii u fi whole number 7 7 o ZTni 1 roP21nt 39 45 C 44525 532 A 15 4899219561 eve195 n581 culate 0445 lt p lt 0533 Answer ymbzal i cay 4415ltp1 5373 Cr EJU II estimated that between 445 J 9535331 61 Edult t inl it gambingoncole easporLts should be madei egal nationwide Comment jnce The con dence interval do 4 c no ltgt 3 ac s 445752 p lt 533 40 9 mains yaluesbelaw and abee39 r 539OThe results are 39incOnclusive 77 7 as To whe rher a maior i ryrof adul rs gt r h i39n k Th39a r g a m b I i39n g Oin co lege ispon rs shouIdrbe made i39llegal i na rionwide39 Example E39srtima re The mean GPA of 12 fieFFaCol lege Sfaf s es Lo studentsusing a 95 quot3 Wf i deWi TWlW W 39 s ruden r survey data Express your39 answer symbolically and verbally V L Ail I I n 39 here 2 5S Cl39hd h39 are sample j A3 wir r39h nI degrees of 39 freedom and a in Two Tails For The TI 83 Calculator o calciulafea confidence 7 39 interval for apopulafrion mean T upress 5 ESTAT177gt gtrTE 5AT45 39 v 7 l 8 TIn rer va7 Enter 1 11 83 Solu39l39ion STAT gtgtTE5TS 39TIn139ertval Enter TInter ual iTI InPt Stats 3 L1st x3 Fr en l Sx4 39 IiiLevel 95 n44 Calculate 39 314ltult342 Answer Sym bolicallyz Srl 4717 3 42 4 ac lamhmll gt V H V a V II u lt he mean GPKTmCSier39r39a Gone 77 g lf r l ig l39i S STUd h liS fig 7 estimated to be be rween 3414 and 34 2 Wi393rih 95 a r LUHI iuence Example Estimate the length of the nor lower le rigfjrlTer average ad lt using a 9confidence 75amplefdata 5 Expr39esisryour anSwerl interval and the following 71 symlgtolieallyand verbally Sample Data 0 engt l f39lower39 le7incm fI om39bac k of bendedquotknee to bo rto mof39heul Answer Sym39b llcally s u Immhmlk gt V I 5 II obtnbblshbb bb itl39T 9r399i 7crcionfidenceJ the l ngth sf the IGW F39EI gldetl f 7 average adult is estimated to beibe tween and 7cm l D i 9 42 4 c o 4 o 70 o Example welve rdi39ffenen riau romobiles 39 were Tested of a speed of 15 i mphforas ropping diVSTgnces ilemeamsfrpppingjjSiameij i r39hecar39vs i nw rhisrsarnpewas 2008 f ee r and The standard 0 deviation was feet Question VE ST Wf i I39 W p mg Vb dis rancefonan ou romob39i le 39 grim6 Lnggm p ed121 go mph TI 83 Solution 6 quotST39ATTFVTESTS 566M bbh b 6b TTIn renval Enter TEMEPEE M VTE egggim 834 HP a a 3 39 888 22938 40 5x284 Sx284 394 M12 n12 C Levelhg Calculate 39 183ltult219 O Answer 39 he mean stopping distance for f 39 an automobile travelinguat a i Speed 9fe157 mphiis estimqted 39 to be within 1813 and 219 E feetwith95sconfidence Example akefa r39andomfsamp leiof 6 istudentssfrlom QlOvonour obbbon bbbl 5 Use your sample and a 95 quot quotC c i fide 2 39 quotih t39 f le to istimatethemeannumberof 1 units SierraiCollege students are enro llazl thHissemest 6613M Results 0 3 quot Share your result s wi39thfthe restjofjherlass bbb bob ybl album 6 7 8 9 10 11 12 13 141516 17 18 19 20


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