Math Elemetary Statitic Review for Fial Exam: Chapter 4 You may brig oe 8.5 x page with ote (both ie) a a calculator. Start by reviewig each of your exam, quizze, a the exam review. The lecture ote are a great reource a well, ice they cotai the iformatio a example that I fi the mot importat. I alo lit ome aitioal review problem from the textbook below. Thee problem are for your beefit oly a will ot be collecte. The fial exam i worth poit a you ca expect it to be about twice a log a a regular exam. Chapter Give a reearch objective, be able to ietify the target populatio() a variable() that ee to be tuie to awer that quetio. Be able to explai why we elect ample to tuy, rather tha tuy the whole populatio (ceu). Give a tuy, be able to ietify whether raom amplig, coveiece amplig, or voluteer amplig wa ue to elect the ample. Be able to ietify raom v. o-raom amplig. Quatitative v. Qualitative a Cotiuou v. Dicrete Variable Obervatioal tuy v. raomize experimet a the beefit of the latter. Kow what a ouble-bli experimet i. Uerta the baic iea behi a biae v. ubiae tuy. Kowig the meaig of volutary bia, elf-iteret bia, ocial acceptability bia, a leaig quetio bia. Kow what a cofouer i, alo calle lurkig variable. Uerta that a correlatio betwee two variable oe t automatically mea that oe variable caue a icreae or ecreae of the other, but that there coul be aother, or everal other, variable that are the actual caue.(ch. 4) Chapter Ch Quiz p.3:, 5, 9, 4 Review Exercie p.3:, 3, 6, 8, 9,, Give a ugroupe quatitative ata et, be able to cotruct a frequecy itributio table with clae of equal with, cotaiig frequecy, relative frequecy, percet, a mipoit colum. Give a frequecy, relative frequecy, or percetage table for a quatitative variable, be able to cotruct a hitogram, bar graph, a polygo. Coverely, give a graph, be able to recotruct the frequecy, relative frequecy, or percetage itributio table. Be able to cotruct a iterpret a tem-a-leaf plot a otplot graph. Review Exercie p.83:, 6, 7a, 8, 9
Chapter 3 Uerta a be able to calculate the mea, meia, moe, taar eviatio, variace, a rage for a ugroupe ata et uig correct otatio ( v.σ ) a correct uit.(stats CALC -VarStat) Skewe a outlier. Kow which parameter are more eitive to outlier. Be able to calculate the mea, taar eviatio, a variace for groupe ata (from a frequecy, relative frequecy, or percetage itributio table) by uig the mipoit a frequecie of the variou clae. Be able to calculate the quartile, the ier quartile rage, the k th percetile, or the percetile rak of a particular ata value for a ata et uig correct otatio a uit. Calculate a iterpret z-core. Give the mea, the taar eviatio, a a iterval of ata value x k to x + k, be able to etermie k (the umber of taar eviatio above a below the mea) a ue Chebyhev Theorem to calculate the miimum percetage ( k ) % of ata value withi k taar eviatio from the mea. Coverely, give a miimum percetage of ata value, be able to etermie k uig Chebyhev' Thm. The fi the iterval of ata value uig k, the mea, a the taar eviatio: x k to x + k. Be able to o calculatio imilar to the previou two item for approximately bell-hape ata uig approximate percetage a the Empirical Rule. Be able to cotruct a boxplot uig your calculator a iterpret it (i it kewe, what i the meia, etc.) Chapter 4 Ch Quiz p.4: All except a 4 Review Exercie p.43: 7, 3 Give paire ata betwee two variable, be able to cotruct a catter plot for the ata. Give paire ata betwee two variable, be able to calculate the equatio of the leat quare regreio lie (a.k.a. the lie of bet fit) for the paire ata uig correct otatio i your equatio. Be able to o thi o the calculator [STAT CALC LiReg(a+bx) ] Be able to ietify the lope a y-itercept i the equatio of the regreio lie a be able to explai, i etail, the rate of chage that the lope preict for u about the epeet a iepeet variable. Be able to graph the regreio lie o the ame graph a the catter iagram. Be able to o thi by-ha. Be able to calculate the liear correlatio coefficiet o the calculator [STAT CALC LiReg(a+bx) ]. Explai whether the liear correlatio i poitive or egative, a whether it iicate a weak, meium, or trog liear relatiohip betwee the epeet a iepeet variable. Be able to ue the regreio equatio to make preictio. Be able to explai the ager of uig liear regreio for makig preictio outie of the omai, provig cauality (that oe variable caue a certai behavior of the other variable), or moelig oliear ata. Ch Quiz p.87:,, 5, 6, 7, 9 Review Exercie p.89: 4
Chapter 5 Be able to raw a tree iagram with probabilitie for a experimet. Give a two-way claificatio table, be able to calculate both margial a coitioal probabilitie either irectly from the table or uig the appropriate geeral formula: P( A a B) P( A B) = P B Be able to explai what the iterectio (a) a uio (or) of two evet are, a give a two-way claificatio table or tree iagram, be able to calculate the probabilitie for the iterectio or uio of two evet either irectly from the table or uig the followig geeral formula: PA ( a B) = PA ( ) PB ( A) PA ( or B) = PA ( ) + PB ( ) PA ( a B) C Be able to explai what the complemet of a evet i, a be able to ue it formula: PA ( ) = PA ( ) Be able to explai what mutually excluive evet are, a how thi relate to the probability of the iterectio a uio of two evet: For mutually excluive evet A a B, PA ( a B ) = o PA ( or B) = PA ( ) + PB ( ) Be able to explai what iepeet evet are, how to tet if two evet are iepeet, a how thi relate to the probability of the iterectio two evet: Chapter 6 Tet: If P A P A B If P( A) P( A B) =, the A a B are iepeet., the A a B are epeet. For iepeet evet A a B, PA ( a B) = PA ( ) PB ( ) Ch Quiz p.35:, 9,,, Review Exercie p.37:,, 3, 7, Give a raom variable, be able to explai whether it i qualitative or quatitative, a be able to claify a quatitative raom variable a icrete or cotiuou. Give a mall populatio a a experimet, be able to fi the probability itributio table for a icrete raom variable uig the give iformatio or by makig a tree iagram (a labelig the tree iagram with the margial, coitioal, a joit probabilitie, uig amplig with or without replacemet). Uig the propertie of a probability, be able to ietify whe a table i the probability itributio for a icrete raom variable. Uig a table or tree-iagram, be able to calculate the probability that a icrete raom variable i a igle value or withi a iterval of value. Be able to fi the mea a taar eviatio of a icrete probability itributio. Be able to iterpret the mea a the expecte value of the variable. Be able to explai what the criteria of a biomial experimet are, a apply thee criteria to pecific ituatio to etermie if a experimet i biomial. ( )
Be able to etermie if a experimet i a biomial experimet by lookig at it tree iagram. Be able to recogize a biomial problem. It i uually a probability problem where we are give a certai percetage or probability p of electig a elemet havig a certai characteritic (which oe ot chage after each electio), a we ee to calculate the probability of electig x out of elemet havig that characteritic. Calculate the probability uig the appropriate formula or program [PRGM -> BINOML83]. Be able to calculate the mea a taar eviatio of a biomial itributio uig the appropriate formula. Be able to iterpret the mea a the expecte umber of uccee out of trial. Chapter 7 Ch Quiz p.7:,, 3, 4, 6, 9,, 5 Be able to explai what the mea a taar eviatio tell u about the ceter a prea of a ormal itributio curve. Be able to explai what the taar ormal itributio i ( µ =, σ = ) Give x, calculate it correpoig z -core, or vice vera. Remember, z tell u the umber of taar eviatio σ that x i from the mea µ : x µ z = x= µ + zσ or o calculator uig PRGM -> NORMAL83 or INVNOR83 σ Be able to calculate the probability that a ormally itribute variable x i over a certai iterval. Draw a picture with correctly labele area a axi. Be able to calculate the appropriate z or x value give the probability or percetage of ata value Be able to explai the ifferece betwee a populatio itributio a a amplig itributio. Be able to obtai the amplig itributio of the ample mea x, a uerta what the axe i uch a amplig itributio repreet. The amplig itributio of x will be approximately ormally itribute whe. The populatio itributio i alreay ormally itribute (regarle of ample ize).. The ample ize take are large 3, regarle of the hape of the populatio itributio. (thi i the Cetral Limit Theorem for Mea). I either cae, µ = µ, σ = σ x x Be able to recogize a probability problem that ue the amplig itributio of all ample mea: you are ake to calculate the probability of electig a imple raom ample of a certai ize that ha a ample mea over a certai iterval, or you are ake to calculate the percetage of imple raom ample of a certai ize that have mea over a certai iterval. Be able to calculate the probability that the ample mea x i over a certai iterval. Be able to explai how we obtai the amplig itributio of the ample proportio ˆp. The amplig itributio of ˆp will be ormally itribute whe p > a q > : the µ = p, σ = p( p) pˆ pˆ
Be able to recogize a probability problem that ue the amplig itributio of all ample proportio: it look imilar to a biomial problem, but rather tha fiig the probability of a certai umber of uccee a we o i a biomial problem, we are ake the fi the probability of electig a ample i which a certai iterval of proportio or percetage of them have a certai characteritic. Calculate the probability that the ample proportio ˆp i over a certai iterval. Ae ormality by uig otplot, boxplot, hitogram, tem-a-leaf plot, a ormal quatile plot. Ch Quiz p.334:, a, 4, Review Exercie p.335: 4, 9, 4 Chapter 8,, a Cofiece Iterval A ample mea x i a poit etimate of a populatio mea µ. A ample proportio ˆp i a poit etimate of a populatio proportio p. A ifferece of ample mea x x i a poit etimate of a ifferece of populatio mea µ µ. A ample mea of ifferece i a poit etimate of a populatio mea ifferece µ. A ifferece of ample prop. pˆ ˆ p i a poit etimate of a ifferece of populatio prop. p p. We cotruct a cofiece iterval uig a ample tatitic (poit etimate), together with ome error, wheever we wat to etimate a ukow populatio parameter: poit etimate ± margi of error Be able to explai what the cofiece level tell u: the percetage of ample of the ame ize that will make cofiece iterval that actually cotai the true populatio parameter; thu, a certai percetage of cofiece iterval will ot cotai the populatio parameter, a we uually ever kow if our ample iterval cotai the populatio parameter, or ot. Be able to ue the appropriate formula to etimate the ample ize eee to cotruct a cofiece iterval for a populatio mea µ with the eire error a cofiece level. Be able to ue the appropriate formula to etimate the ample ize eee to cotruct a cofiece iterval for a populatio proportio p with the eire error a cofiece level. For the mot coervative etimate (or whe we o t have ay ˆp available), ue p ˆ =.5. To ecreae the error i a cofiece iterval etimate:. Icreae the ample ize (preferre, but ot alway ecoomical or poible).. Decreae the cofiece level. Be able to calculate cofiece iterval for oe populatio mea µ, oe populatio proportio p, the ifferece betwee two populatio mea µ µ, the ifferece betwee two populatio proportio p p, or the populatio mea ifferece µ, uig the formula a/or the calculator, a write your awer i the form of a etaile etece a we i i-cla (ex. we are 95% cofiet that the true populatio mea of... i betwee... a...). Remember, whe writig cocluio for the cofiece iterval for two populatio make a compario betwee the populatio parameter of the firt a eco populatio itea of uig the wor ifferet or ifferece. You houl alo avoi uig egative umber i your fial cocluio. Ue the appropriate ivere program to get the z or the t whe uig the formula:
Deire Etimate: Cof. It. for µ Cof. It. for µ Cof. It. for p Aumptio: Ditributio: Formula: Program:. SRS. > 3 or populatio i ormal 3. σ kow. SRS. > 3 or populatio i ormal 3. σ ukow,. SRS. p ˆ > a ( pˆ ) > z itributio t itributio f = z itributio x x ± ± t pˆ ± z z σ pq ˆˆ ZIterval TIterval -PropZIt Cof. It. for µ µ. Iepeet SRS., > 3 or pop. ormal 3. σ, σ ukow, a, kow t itributio f = mallet - ( ) x x ± t + -SampTIt (ot poole). Paire SRS. 3 or Cof. It. for pop. of iff. ormal µ 3. σ ukow, kow. Iepeet SRS Cof. It. for. Each pop. ize p p 3. Two categorie with at leat i each. Note: SRS = Simple Raom Sample t itributio f = z itributio ± t pq ˆˆ pˆq ˆ ( pˆ pˆ ) ± z + TIterval -PropZIt Chapter 9,,, 4 Hypothei Tet A hypothei tet i a proceure that help u make a eciio regarig tatemet mae about the characteritic of a populatio. Be able to perform hypothei tet about a igle populatio mea µ, a igle populatio proportio p, the ifferece betwee two populatio mea µ µ, the ifferece betwee two populatio proportio p p, the populatio mea ifferece µ, a gooe of fit tet, tet of iepeece, a a aalyi of variace tet (ANOVA), uig the eight-tep proceure: 8-Step Proceure for Performig a Hypothei Tet: ) State the ull a alterative hypothee of the tet. ) Chooe a/or tate the igificace level α. 3) State type of tet, the taarize amplig itributio that houl be ue, a check that all of the require aumptio for uig that itributio are atifie. 4) Compute the tet tatitic. 5) Draw a picture of the taarize amplig itributio you are uig. Label the tet tatitic. 6) Calculate the P-value.
7) Iterpret the P-value a make a eciio. If P-value < α the we reject the ull hypothei, a we have ufficiet eviece for the alterative hypothei. If P-value > α the we o NOT reject the ull hypothei, a we o NOT have ufficiet eviece for the alterative hypothei. 8) State a cocluio i the form of a etaile etece that aree the alterative hypothei. Whe we Reject H, we ay there i ufficiet eviece to how that H, where H i tate i wor. Whe we Fail to Reject H, we ay there i ot ufficiet eviece to how that H, where H i tate i wor. Type of Tet: Aumptio: Ditributio: Detail: Tet about µ : H : µ = value H : µ value µ < value µ > value Tet about µ : H : µ = value H : µ value µ < value µ > value Tet about p : H : p = value H : p value p < value p > value Tet about µ µ : H : µ µ = H : µ µ µ µ < µ µ >. SRS. > 3 or pop. i ormal 3. σ kow. SRS. > 3 or pop. i ormal 3. σ ot kow, kow. SRS. p > a ( p) >. Iepeet SRS., > 3 or pop. Normal 3. σ, σ ukow,, kow z itributio t itributio f = z itributio t itributio f= - for mallet or ue calculator to fi f (it will be ifferet) P-Value: Normal83, or ZTet P-Value: T83, or TTet P-Value: T83, or -PropZTet t x µ z = σ z = = x µ t = pˆ p p( p) ( x x ) ( µ µ ) + P-Value: : T83, or -SampTTet (ot poole)
Chapter 9,,, 4 (cotiue) Type of Tet: Aumptio: Ditributio: Detail: Tet about µ :. Paire SRS Critical Value(): TINVRS83. H : µ = > 3 or t itributio pop. of iff. µ t = ormal H : µ 3. σ f = µ < ukow, P-Value: TTet µ > kow Critical Value(): INVNOR83 Tet about p p : H : p p = H : p p p p < p p >. Iepeet SRS. p ˆ > 5, q ˆ > 5 p ˆ > 5, q ˆ > 5 z itributio z = ( pˆ pˆ) ( p p) p( p) ( + ) p = x+ x, + P-Value: INVNOR83, or INVNOR83, or -PropZTet Gooe of Fit Tet H : Pop. fit expecte itr. H : Pop. oe ot fit expecte itr.. SRS. All expecte frequecie 5 χ itributio f = k ( O E) E where each E = p P-Value: CHI83, or GOODFT83, or χ GOF-Tet Tet of Iepeece H : Two characteritic of a populatio are iepeet H : Two characteritic of a populatio are epeet.. SRS. All expecte frequecie 5 χ itributio f = ( R )( C ) E = ( O E) E where each ( Row Total)( Colum Total) Sample Size P-Value: CHI83, or CHITST83 or χ -Tet Aalyi of Variace (ANOVA) H : 3+ Pop. mea are all equal. Iepeet SRS. Pop. ormal 3. σ are all equal F -itributio P-Value a ANOVA H : 3+ Pop. mea are ot all equal
Chapter 9,,, 4 (cotiue) Be able to recogize whe two ample are electe iepeetly, a whe paire ample are electe epeetly. Notice that may of the tet tatitic for mea a proportio meaure the umber of taar eviatio i the amplig itributio that the ample tatitic i from the ull hypothei value, which meaure the eviece agait H. (ample tat) (ull hypothei value) tet tat = (tev of amplig itributio) Sice we ue a raom ample i a hypothei tet, there i alway a chace that we make the wrog the eciio i ay hypothei tet we perform: Type I error: Deciig to reject H whe H i actually true. Type II error: Deciig to fail-to-reject H whe H i actually fale (whe H i actually true). Bae o your cocluio to a hypothei tet, be able to ietify whether a type I or type II error coul have bee mae. Be able to explai what the igificace level (α ) meaure. Remember, it i the probability of makig a type I error. I other wor, aumig the ull hypothei i true, it i the percetage of all imple raom ample that coul have bee electe that woul have lea u to makig the type I error of rejectig the ull hypothei whe it i true. Extra Practice Problem o Cofiece Iterval a Hypothei Tetig Chapter 8 Chapter Quiz: All problem but 4, 7, a 9. Review Exercie: All problem but 5, a 9. Chapter 9 Chapter Quiz: All problem but 4 a 5. Review Exercie: All problem but 5, 6, a 9. Chapter Chapter Quiz: All problem. Review Exercie: All problem. Chapter Chapter Quiz: All problem but, 6, a 5. Review Exercie: All problem but 3 a 5. Chapter Chapter Quiz: All problem but 3. Review Exercie: All problem but 7-4.