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Worksheets for chapter 1 + 2 (Examples with answers)

by: Brittany Wittrock

Worksheets for chapter 1 + 2 (Examples with answers) STAT 239

Marketplace > St. Cloud State University > Statistics > STAT 239 > Worksheets for chapter 1 2 Examples with answers
Brittany Wittrock
GPA 4.0
Statistics for the Biological and Physical Sciences
Ernst, Michael

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About this Document

All the worksheets that were handed out in class as examples. Answers are on the sheets
Statistics for the Biological and Physical Sciences
Ernst, Michael
Class Notes
25 ?




Popular in Statistics for the Biological and Physical Sciences

Popular in Statistics

This 18 page Class Notes was uploaded by Brittany Wittrock on Wednesday September 16, 2015. The Class Notes belongs to STAT 239 at St. Cloud State University taught by Ernst, Michael in Fall 2015. Since its upload, it has received 36 views. For similar materials see Statistics for the Biological and Physical Sciences in Statistics at St. Cloud State University.


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Date Created: 09/16/15
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39 39nuetigating thie gait What are the easee A a bet uarabies and is aeh quantitative at eategerieal e at a a g e r Y K e What might a dataeet ier like that might inein U5 anawet this neetin Make up game data te shew time first mule at rawa at each a dataeett E Sectln 12 Sampling fro Ppulatmn Example 1 Number of Cell h ne cells per Ba Princetu Suwey Research reperts en a suruegir 4191 sell hne users ntheFUS ee dueteu in May 201E1eslltng f nen sereeedeu ebeut hew merw phene cells tie yeu malig anti reeeu n uur eel m p n E M a What is the sample iri this study Example 2 Driving with e Pet 1 yew lee uer 3 peeple eertieie ted in an enlin pill en ennrm cenduetee n eeril 21312 eskinr Have ye u ti quotl 1 ever driven with et en your lap We see ith as ef quotthe artieiants nswereciyes ml 65 answered nee i n 1 r Lr What Is the sample bin Can we ceneude that uf 3 drivers have d iiren with e pet err their p er 391 A l v A39s s n all39 5 H r 1 A L r u l l l i results te all drivers er even re s 3 Explain why i 5 net eereprete te eneraliz tines drivers whe uisil euneem What is thepreiem with thismeth if data celletilgn cl Hew might we select a seer f pewpe tht weulrl give us results that we can generalize t e breederpepulatien up age 2 Quick SelfQuiz Sampling Bias rat wish t estimate the numeral 3 t i tht staents at year anisersityrsagntl studyin methad belawj indicate whether the results are Iker ta be F JDFESE tatUE etthe entire student sahii ar whither the metha is likely ta give lease results Fr Each sampin ht a ask students at fin at the lihra rt an a Fritl at b k Stuantg Wm is at 3 P3 W W TUIde night tSJ 5 sq f Semi ah email Lit ta all students and as al the respahses we get i greaal Example ubiis Spear t Be a Hw a questah s wartied can have a ramatt impact an the result These twe questiens appear ta be asking the same thin i quota yea think th sheutl Kai i quotL yeti think the US sheud at teri gable spehs aanst elemeer r to the frst austiea while amast n public speeches against demeraeg w it Iziweaer 21 saicl such speeches Sh ud bE alawd in mm deuble that 39 sai such seeehes shaultl net e ferhdtieh in answer ta the seenti questh Why CID yeti think the results were an different Quick SelfHi Wrding Bias 3 a survey 5 ta V C nelueteti usih a rahtlem sample f etzehs ih a tewri asltih them it they asuaeart rising tastes ta hereas funding tr the pale sehel w uestan in a waythat islikelg ta hiasthe results 1 5 g a a ward re re yes answers 39 25 fir 4 g Al l Write th Llesteh in a was that is likel s the resuts tewr rd mere h answers v j t t H 1 Vt l f A L l i r r at l M h r 3 PH L Y i a l E 39 l A it a I A t i 39 E 7 r r r 1 A W V W n i E 7 A t I 1 J 7 a r 7 75 1 f n r P n m j FJHLVH LL 7 r V g N gs J l in practise at eeurs we sheultl try ta actually write qu5ti 5 in a was that wl NOT bias the results Ir The first step is ta retagna th ettett f leadin questiehs 39fbservtional tudies Section 13 Ee rimems and Example I ssmietien er Causetien Far eaeh at the iellewing statemhts indeate whether the statement replies causatieh erjust irritates asseatiah withe ut causatian a yeti study mere your grade will impraae ih this teurse JI LA Y Vi a a a u l it 3913 Witt ta lees rink ta 2 5 L A gt j 7 J 7 r 39 l L I r C heir th braia tends la L ege eduetn elated in peple with a Ca Hermie 2 Telfevisien sets and Life expectancy Ther is a quotwere stren sit39ae asseeatih hetweerl telea isien sets her persen in a euntwr aha the ite sheetancy ef the pee ple it that E uiiiitw which means peeple in eeulhtries with lets 9f Wstend ta litre lehger a ees this meah we can impres the life speetancy at heele in evelean eeuntries by its i EIEHlSi sets d r sendih there truly escre a assihle Etttif tmdln aariahle h thisassaeatiem I J IQE g l 1 Exempie Bees Kindergare Lead to Erin s a stte Iegislter in New Hampshre elameti in July 2012 that ltnclerga rteh prerarhs lead ta mare UdEi iEE that thelarest ei ii the temmhhties irI curate was the HIM K legram and alse ha mthe mast crime aji W at eemrhen mstake s the lgislater melting 39 h39 V 5 39 it 1 fl aft A 7 1 n j K J r 39a 4 391 39 essihl enteunding 1aarialale in this asseet er mei H netd as C mmunity with a khtlerg39i 1 last 9 39 t h scih r 39 edit 9 meta Quick SEEQuiz Assecietien Causation and Conjeunding Veriebies ser hetl h each case hiditate en assetilateh is Cl 3 Whether the statement implies ta usatiert eriust asseeaten h a pessihle tertietmtiihg aarhe Mere sales 4i sansereeh teed te wear when mere sunglasses are seltli quotExercis treatises risk at eithemers Clams a hetJlirl reperting in steely at elerly heap that retarded hew mush each exercise at age as he thn whether the person gt elahmeris d seas n L quot13 L ail E 39 L E mint n 17n7 57le P7 r H 139 LEJC r39E1 L J RH a A r 39 quot74 7 q r l A r r ri es 2 Example 4 Exercise and Deprssien Ir eeeh ease helewi we describe a study te etermine whether eserei se helps increase erteih me nhehcin ehemees h the brains heieet whether each deserihes an experiment er n ehsersretiehei study all We eehteet e rehelem sample et 1 peeple r1 reeerel hew mesh eeeh persh eeereises ahel else measure the chemicals h the bran fer e eh eersen i v r r 11 1 L V l l J r r r 3 h Use 3 rehtlesm same ef f peeple we rehtiemy essn helf ef them he rtieipete ih e regular eserese preterm Fer si xweh eeri whe the ether hef makes h ehahes let the end ef the time pereei we measure the rein chemieels Example r Ce ein 2 end teeming re geiemis er a te test this ve ell cletilsj ihelerlihg the use ef rile ee v e L a quotre te Wtk with Example ls the rmnent Heed Stranger Desehei g 39rs eseermeht te see if right heed strength s reeter then leftheme strength in righthanded eeple tree have a handri te measure strength errel 3 rightheeded eeeele t use in veer steely e sure te iheluele hew re hemeaten is used r1 seer tiesige su u AlAlLIIAI msLL AIs ll IAII 4I44 1 m Mm Quick Selfuh Hendemized Experiments grimehat te determine whether tahhg vitamih n suppements esigh e r39andeh ized eemperetiee else 5 helps memew tee have 40 eepl te use hr the stung he the study w il tehe peee ever me me nth Section gategorcal Vriables Example 1 Talking Ahoy t Spares c Survey ih Newemher 12 Backed a rendem cam cf 2 U5 acicltc Hew efteh dc yen tlh abut Sec r115 with fa mily and frienc The reeute re given 1 the fellewihg fFE QUEn y tam r Eneepenee Freq UQEHCEF W Every day er nearly every clay L 302 heutehce week 277 Occaciehally e 526 Rarely er newer W 395 TTAL 20c a What prrtien rarely er never Mk abeut sperm we 25 b What percent 1 peeple h the ca 9 5 r C Gim Quick SelfQuiz Frequency and Relative Frequency Tabfes he a mi ta ste test peeple wer NEW Fcur Ji e reht types cf water am asked te select their tcp Cheice ell elf th pa rticpe rite Selected tap weter S Eecte Agua fjna it seemed Fiji and 24 selected Sam s Chcice r 7 F rugn39i gi J a Isplai 1 regents Eh a frequency table Ilr39i VL 1 b What Jr w t z sewt page 2 Example REMIHHShf Status and Gender 169 eellee students were asked ahaut relatihshia status and gehder The results are hel argatF tablet l39aen in the fellawihg Female e Mle Tetl la a relatlehshia V 1 i a2 tile templeate 412 Tquot w snge e Teta 19 a Whvt preperrtln at students h this sample are in quot h l V 4 r 4 j I y l r i A LA quot J pe are r is 1 5 r H F r r A Y A A L11 rr 1 r L L 5 A I r quot 1 I r F quot 39 J a 4 l 7 l 7 IV Lk J u alt What prertih af the peeale whe are inna ratiehshp in tr d What praprtizn at malee h this sample are in a re l mu e e Usin g represeht the preertleh ef females in a relatiahs yw and 355M 1 rear L a prpertien at maes n a relatlehsh ipf Feel the differehee h rapert iehs V 39 Example 3 Hendedness end Decupetfn h a study ef handed ness Ln eeeu patients 10 eataf il ipsythlatrists we re lftahal 26 a V 14B arehteEts weld E at 132 arthepedie sureahs we re left handet and 1amp6 M15an rs wwerelefthahIrletl i 0 ll 1 thrll 1 7 r I A A J r 3 la n f n a A r t lEF r J WV V I7 1 7 77 7 r n n u s q r l4 r m u A 4 J 7 l L j l r J f1 39 w A 1 elijle m the L e I H Quick Selm lf Finding w km TumWay mars Errars in meeal preser39pti ehs eeear relatively fI EUE thF h a study tw reds at ete rs had simttar Err r rates arr ehe greup switched t eprescritiehs while the ether carrtlhaed with hahewrttten preseriptiehsm hreh in the tweensay ta ale Cline agar Iter the number at errers was measured The results ar r Errr 39 at 3594 zrar el 2370 7quot Fl r t Ilgt J 1 1 J J Jr 1 l Eeetrene l 1 Written a H n the raw and elumn tetale h What preartlen af all the eireserptiehs 3r in d What preprtiah ef wrtten preserltlehs 7 w e Wht repartieh thee Vi blehape nd Center SectiWn ne Exampfe 1 Height ef Students The h etere m and detelet her berth shew the delta fer the emanatitewe we riehle Height fer studehte a eeerbe the EHEFI shape efthe isletrbutieh 1 h raw 3 Smeth curve evr the histegrem shewing the ener Shape ee Fri g Hewemey E39 F l I A 7 g l I 1 1e I r g 1 k E r J w FligllillIiiIIIiliiiiii iliiili l r e Ililiiliiiirli iiliililiiliillil lil i QEIi 1 39iiiiiiiiliiili iliiiII39IIIi39IIii IIIIEI IiEIIGIlli III I il illllllllill Il ili39iliii l iii il l I III IIII IIIIIIFIII I II IIIKIIIEI II I i 39i I PI l r lt 1 a r r r lliillili39liii fli39liiiEl lli llll 1ijil Iiiilllllilllllilull A w L A J LL 39lililiIiiIlliilhl lliIEI IIiii39ii L El39illllililll39lilll Ill l1 1 11 r r ILIiIIII39IiI I I Iil 1 III I III I39 ll PI J 1 1 FM el1 u 7 I It I I I3 e1 e 5e ea 5 L11 ee Heeght i Y i v 1 quot quot r 1 an Innquot nunmnmuhuiiei Ii galaIII e 3e Height Example HeHywad Meeies Warm Gmes It Weri r055 neeme frem el eewers n milliehe ef News 01f 4 memes te eme em ef Hellywed in 20131 is shewn in the etplet lHIIHIIiI neigeliiniii gs A lt 4 I 1 lt j j 4 51 44 EI E r 1 A by L r I 63 F 393 A ll QLETDL e gquot A L 1 3 F 7 j V Y r L quot1 n iijj L r r u 39 w 7 quot I39L 7 u 7 r 1 J r h 39 L L L r 7 7 r gt r L 1 r F quot e LA 39 yew u Equot a EL 0 quot121e a 339 4 I Ef e 4 EU DU 1 E fterhd 3l1eeee Mini a Describe th shape ef thedetr huti gi f if fi f 39 fiu fiii Ffvr b 0 there eepear m be iutlilere If Se eeuee nick SeifQufz Shape Of a Distributmn The number ef theaters t shew e meme durin eenng weekend fer ell mevies te eme em ef HeHEeWUj in 2011 5 she we in the detpet eeerihe the shape 0f the dietrihutien e jJ V EFF r1 in r H A II 49quot i ee ii leieeIII A fer E e I PIJ Y I V A 1 Jae 1 AL Era 7 77 H 7 7 quotgr 7 r 3 WW y eater w 1 e 1 rednu f 1 1P5 55 r y r A r A r A r r u lt 1 x E A L A L A A M g 45 1 1 S39 r page 2 EXampIe 3 ats an a sandwich The numer at ants elimhin an piece at a reenat butter sanaw eh Eett an the greens hear tn anthi li fer few minutes was measured 739 differe nt times and th EELIIts a re a Calleatate the mean humer at a e Suppese ene ef the quotwish hits was eetremew appei numher ef nts fr tht hit was actually 15 giving the 7 vanes as H1591 223 w dataset and eemnare year answers to Wejprevinus answers LEE I ii in far n Exempie 4 Warm Grass af Hie ywaad Maurieth reefsted a aatplet efwerlel grass Meme frarn meaies is shwn n Esampe a Estimate the martian warts ress tinsame Quick Selfate Mean na39 Meter 1 Sandwich ants restate The same persen whe wanted the number at ants an peanut hatter san wches eseribed in Example 3 asa canted the namher at ants an Ham ntzl Pek les sanwehes The RIMES a1 What is n r a E r n EL 1 s 39r t r 1 39Iquot tquot A E L F a I If r quot 39539 J v 5 r v a 7 t L 5 p a CFFEQWEJLQLLLhi elrs tethse n Eta mpe 3 tie ants seem to prefer anut hutrsatndwiehcs afham and stakes sndwtehaef 2 Deanne Weekend at tltywead Meatless rees ite a eletpl t number at theaters epntng weekend tar maies 39s Sh W in the Luek SlitQua n thv a Estrnte the medin numer at theaters Greening weaken page 2 uck Selj Quiz E SEE and VrmeE Give thecges and theyartablesjn each Situatim be w 1nd identifyquot each uariabie as Eategmical Jr ua t LH 1 A 1 I m l W a g kt g mtgem whether EH mt thy supmrt gun mntml Q r39 1 l 7 E g l L tju E 5 ExamJle 2 Revisited Yagwt and Waight Lass Can eating a yagurt a day cuse peaple m Inge weght In a study Enuegtigatng thS What 5 the Halanwr A variable Quick SelfQuiz Excln twy and Response Variables n a h situat n indicate the expl atnw ya table and the resp nse tiara ble a BEES mdtatkn hep reduce EtrSS r A r r r 1 539 n 395 b Is hyperactivity in children affected by Sugar mnsumptim39 eds ures Sprea Emmpie 1 Tps far a Pizza De iivery Persian A pizza delivery DEED reed rde ail at her tie an ether aa riablei raver ewe ral Shi ite She i39eeusaea the teauits and much mere eh ia w at Pitta Girl en the Slice wesite The are riahle Tip in the PizzaGri taaet iheiudea the 1214 tilde she i39C ilz dEd ahd the aaluea are lee even heldw Use tethndhwaF td thd the wean and m1 FJ gt gt JEN Inf Emmp e 2 Fewer Hf My Fat i Me ht made Lip at heady fat fat 1 then Fer this sample the mead petteht htmttliri fat 35 196 add the standard devitidn is H The diatrdtidh at the The are tiahle Beddet in the Eddttliat dataset EVES the etceht at we thatr fat arides a ruhly symmetrit and hailshped If tree are en a damp uteri check this a Fat an intera that liker td tdhtan EQUINE 95 at th data values 33 The argegt petteht laddetail at am man in the sampiriy amiiet is 37 Find and hterpret the Z SC re fer each at theae aa Idea Which is reattiaeaF L e Sandra Samaritan dram hedw ahewa the datath th quantitatae variable Height tat students e s 3 ht f il quot merged in the 5a male and US ur estimated Quick SeifQuiz Estimating Mean and The hist r rte1 T f ElIP a Eatimate th wea ihd the atahth gigsav m Emma he aue ef the maa39m values at mean and Sta dar r 4 J r a at W qfu39 39f I39HJ a ll 4 L LL l ALA wee Hemp 3 Tips fer Pizza Gir revieted revtet th date g ve fer tips fer a eizze girlt Even in Exemle it ZEN 55hr Fri r r F quot1 r1 e 3 I n n 1 n w technetgy te fm the fwe number summery A seere ef 1011 en the SIM Methemetiee Ge er el Teet is at the it peree tie tr e eetlee taking the SAT Cleari y emplan in te rme ef SAT seeree whet t me 15 to be quotat th 15 ereentite 6 1C 45 t g t 1 r j L 7 J r 7 1 r A r A I I m li 1 H V r 392 V A V J 1 W t Iquot 1 391 t t 1 t n E p E I Fr each ve number summary belew indicate whethr the data appear te be symmetrie skewed ID the riht er ekwe tn the ett 3 1L39 5 35a 33 93 i3 J 4 EL 10 13 at 20 550 t I39 j t A 1 J 1 t w 39 39 t F 7 J t r I a er sicton 24 Lutliers Boxplots and uantitativeCateoricl Relationshis Example 1 Pee we Hem ef 5 rates Th fee number summery fr the DDEM IHHS ef the 51 US stats ilh miliehs f eeeee is J it 660 l E E3163 35 ees stermihe whether there ere ehyteetliiers art it 5 identify them eese 1 first test 122 use M21 u lat Elise sent Tquot 41 reset eases witem w Ei LeviL12 f m Eta 1231 e131 13 r 1J4 quot39 e 139 x 3524 4 n SEW t sees L 114 attempts 2 Grass State Precinct The herselt shews the Grass State Predu et ESP per eepite ih eters her rstdeht fer the 51 eL ere there any utters is set eepretmetely what re the i values if the eutliers h Estimte the range of the ete end estimete the QR fer I the dated 1 Estimate the medeh f the date rested weseee seine steed eesee see 9 ees the date appear te he symmetric skewed rte tha left skewed tel the right er hehe ef these e e yeu expect the mean te he greetr then r less the the medieh l Quirk Seffiauis Understendfng Emrplets The WK WIDW 5 a graph fth DEFCEM E the ulatieh te red Lite high seheet it t eeeh ef the 50 stetes F t cutlets e ere there he f w 1 Estimate the range et the ete eeues c Estmate the meeh ef the date st est estimate et d Which of thw fellwing values is the t the standerd detriet39reh 1 1 E 12 9 E 94 t e e 4 en High cheela pepe 2 Example Smokers by H39gien of the Ceuntry in the The sideaiyeee explet ehewe the percent pf eduit reeiciente whe smoke in each State etegerizee he regri pf 1th eeuntrv Midwest Hertheeet Se uth er West iph Seeme t1 have the ff Oped h h h whieh repien is th State with the higheet Hw 4 in up e e eea i Ft Regine 39w i 1e 15 ee 3 luck Selfpie Que tite tiveCetgerimi Heietienship in e reeet study ertiepehts were ranemized te rink either tee er eeffee were dv fer tw weeks utter tw weeks biped sempieswJrEeepeeed teen entin and an immune System respense wee meeeuree with hgher we 45 re pr sehtihg e etrenker mmune system e apes there appear te be e reletienship betweeh th eetegerieel erebi it er eeftee and the uenttetv e we riehie immune reeplnee Eetfee i 1 hi Which rpup eppeers te heir the etrehger immune repense w 1 H E LE e I Hi EU Elli E d eeeriptiee statieties fer the Steely re Shewm Give neteten fer and fn te ifferenee in rhea variable Deiek H Ht Mean SE Mean St ee Minimum 91 Me ien Q3 Interfere eeme eifee 1 D u39 Tee 11 i r f i i Maximum 52 15 ES Dt 225 1556 EEtEE 52590 Ef e Eli a E 13 EED 55 Sigi El Dim CURE GDEFF W Eil if GGHFI CDEFF IE l ill 39 Ar m a I39EI39 m quotaquot If 3 2 3 4b 5 httpwwwisti sgnetCmrrelatiams 4 ul 4 4 lulll 1 1 u 4 lJ ll4 n Section T10 L uanttative Varia catterplo Carrel tion Example 1 PositiveNegative Assacfetiens ln lath ea 5e a 1tau expect a aaatiae er negatlve aaaeetat ian etweerl th twa quantitative quotua rialaea a Number at years at e ueatlan and annual Slam Far US ajulta Tr it at la age and maximum running speed far a ulta 1 ME a race and maaimum runn39n peed tar chlaren Imp05ml u E d ae af the haa ntl an age at the wife fer married eauelea Pg u Example Scatterfeta and Earrele en Fr aeh at the ageatterplata wheh ef the tellawi 7 1 E A L 2 a aaraaimatea WE errelatien at the data Shawn 1 title ii 13 i ii quotif 14 12 a a lar a U39ll Quick Seifa ufa Understanding Saetterla ta The aea tteralt ahawa the relatlanahip betwrn numbr elf rebaunda in a aeaan and fre threw percentage tar payera in the Ntena Basketball Agaiaciaten 53 a at the Scatterplet The aattm rteht 1 11 kt l I i A r n 3 aaszttiae r negative a aa 39 il quot a quot I I t I EET SLED E39 EEEIU i 39iU EIEEIEEI Heltruuae all Wlnieh value is the beat gueaa at the earrelatin 7 r L r x l e Which at thre aaluea listed a part a re i maeaaibl aaluea tar a aarrelatan 4 Lara 143 a What can we any be ut a layer rereaentd la the tap left h Laea the directen afaaaaeaten apper ta be mere 4 ul 4 4 lulll 1 1 u 4 lJ ll4 n Section T10 L uanttative Varia catterplo Carrel tion Example 1 PositiveNegative Assacfetiens ln lath ea 5e a 1tau expect a aaatiae er negatlve aaaeetat ian etweerl th twa quantitative quotua rialaea a Number at years at e ueatlan and annual Slam Far US ajulta Tr it at la age and maximum running speed far a ulta 1 ME a race and maaimum runn39n peed tar chlaren Imp05ml u E d ae af the haa ntl an age at the wife fer married eauelea Pg u Example Scatterfeta and Earrele en Fr aeh at the ageatterplata wheh ef the tellawi 7 1 E A L 2 a aaraaimatea WE errelatien at the data Shawn 1 title ii 13 i ii quotif 14 12 a a lar a U39ll Quick Seifa ufa Understanding Saetterla ta The aea tteralt ahawa the relatlanahip betwrn numbr elf rebaunda in a aeaan and fre threw percentage tar payera in the Ntena Basketball Agaiaciaten 53 a at the Scatterplet The aattm rteht 1 11 kt l I i A r n 3 aaszttiae r negative a aa 39 il quot a quot I I t I EET SLED E39 EEEIU i 39iU EIEEIEEI Heltruuae all Wlnieh value is the beat gueaa at the earrelatin 7 r L r x l e Which at thre aaluea listed a part a re i maeaaibl aaluea tar a aarrelatan 4 Lara 143 a What can we any be ut a layer rereaentd la the tap left h Laea the directen afaaaaeaten apper ta be mere pee Example 3 Carreftfen and Dut ers Use teehnetgy te nd thu eerreetien ef the fielwhsg data SE1 wW E e Eeeeluee ifquot New nd the eearreeteh Fer the ewe dateeetg hut wth the eutei 50 remeu ed eewihg h 5 petite e we 2 1 1 Cemmeht en the e egtefni g Example 4 TV and Le Expectancy w Fer e sample ef eeuntrtes we have value fr the emerge fe exeeeteney n yea re and the preveiehee ef terleeeeh sets number 2t W3 per 1000 peelet The resuts are depleved in the Seatterplt belew quoti g r L Lr 7 rl3941r394ii L 1 L 1 1 BE it A t t Jig Ktnger L f minted Siafe 11 Mexie rue rhedie V 439 i Mdegeeeer f Life Expecteney i H quotti r i aehe r 074 i Seuth em ee 50 4E i Angela u I 11 t I39 F D 400 810 300 1 U er t a eeee ethege ue at 5 there per te be en essecietin between the twe variables If 5 ie it pes i tiue b leeed eh thee results eemment en a prepesel t send mere We te ceuntriee with Iwr Ife etency te hlp peeple in theee eeuhtrie live I he r i E Kr


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All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.