Exam 2 Cheat Sheet - Business Statistics | BMGT 230B, Study notes of Business Statistics

Download Exam 2 Cheat Sheet - Business Statistics | BMGT 230B and more Study notes Business Statistics in PDF only on Docsity! Chapter 8: Random Variables and Probability Models a Mean: 1 =T.) z + Binomial coefficient ia *'* oh Grech ett mu (fermen) © “Tinamial Distribntion Formnta © Pepulation meen a © Variance: of - Var0 ‘oo tle sigma (For standard devia © Population vance © The weighted average of the squared deviations (x u)'2 of the vanabl the variance. the mest scatiered the vrhnes of X ar on average © Fea disicte manda vata le. 2 Diy = SA pagan ry of x euecesses in x trials successes in sample fr fis meaa y. sent on akon im —aeitor 6 Buin gone! Va) = EK y= ROS Eos uern the expected squared distance Beam . 1 Rinles for means and variances + Varizace~ aga, standard devistion ~ cqprvasiance) © AddsuaSublaticn, ‘© The binomial sampling distribution for counts can be used when the ef the population, because the » observations ample 1 seller than 10%. ill be nearly independent wien the size of the por ation isch lager than the sire ofthe sample 6 Miitiptienion Normal Distributions GX) —akx) ‘Bell chaped. symmetrical, mean = median = mode 1 Yat “eva + Location determined ty the mean, spreed determin __ of SDaX)=IaresDoQ, © Probability is mzacured by the ares under the curve © Its erandom variable and a and D are fed muscber, then Standard Normal Distribution, theZ distribution * . is defined to be 0, Standard deviation is 1 va independent random variables then REQ) !EC¥) 8 Va Va VartY) © Thestandarel deviation af a random variable ie SDEX}= SQRTVartx)) © Empurcal ole © PC ieZ=1)~ 68 5 Perera 9 © Pi3<Z<3)- 997 Binomial Distribution + General Characteristics ‘Atal has only two possible outcomes — “success” 9°” co There isa fixed sumber. 2 of :denticz! trials na 8 Theta of teexporiment me pendent feeb ther + Tran om mrs bain: 2 | © Theprolclay of «swum. ecco to Ua (© Tfproprescats ths probability of a sucezss, thea (I-p) = q is the probatilty of a failure Chapter 10; Testing Hypotheses about Proportions > Satsment1)= nul iypethens ithe esa 2) > Slam 2)—alenatve hypothesis hen fx) ‘Two Mahods of Hypothes Testing Chapier 9: Sampling Distributions smd Confidence Titervisls for Proportions 1. Using p-vatues: 9. Roles for Sample Proportion © Cale tet {Ce tat Fal pvr ec ae el . mpare to 1 or a/2 (one sided or two sided) 2 te proportion » of sue 2. Using cntical veluss: 6 Scket nope * Conte the cafidence intra confidence Interval ofa Sample Proportion fps yw the concentra FIR Hic poste the eonlence mere jet He ; Tete foc popultion pesparon vy? = 9 Npandng>9 . aN 2 95% confidence > 95% of samples of this size will produce confidence intervals thet cap 2 - ‘ture the true proportion of the population (and we =xpect 5% of sur samples to produce on as itera st fio apr the tv roporson : 2 Mavs af emor 22 SE(B) Orble te it ofthe CL wich teeta the © Coxfidence tri to et ypotes Me Fou Sipe tr ype . Te + Assumptions nd Condiinns > Define the Ispoteses to ext, andthe reqied 2 Independence Amun: Ae imple stern dependent of each eter? and he required egifieance lee! > ‘Was the sample randomly generated? 2. Caleolate the value of the test statistic. 9 1084Condion Trampling dae without eplceent then th ample si. mus Be 3 Ti thers beod onthe ebro datz tvs IO the opin : > Tins the pale bs » SuetesFalic Conon: Tiesaup sem telaneenrietia tae a (hs? yao ton leo the th th vee, Tee earth alae the renge te evidence again! the mulliypothesisand the oe cofient you cas Be + Sane sz fora dies matin of wor - N\a.5-pIR) = n={=") ped-v9) about your ntespetation , © The magnitude or size of an effect relates to the real-life relevance of the phenomenon uncovered. © shenpicanbnonn,wsep= |b reer cert ‘The p-value does NOT asseee the relevance of the effect, aor ite magnitude, © cae Zable For means use when cis known || «Type Lerror eget and thal Hypothesis w ect tev ncouctly ees ts Vas (So corso Ponca . : annie ee iaea | 2 The pebablty of aang x Type ane ih gic level |] «A Type MH error fail to rejact and the ull hypothesis is false (:ncomectly keep 3 false He) @ @ Conf Tat al ig Lev Conf Ley _42 for 2 7 0% 2 The probability of making a Type II exroris labeled 8. The power ala lest is T= 9 Reducing a seduces the power of 2 test and thus increases 6, Chapter 11: Confidence Intervals and Hypothesis Tests for Means © Standard deviation= s/\/n, and is called sampling enraged js puller tha * se if the population by a factor of vn. =O Xtr%*o / vn «The mean=. Mean of all ¥ 1s pretty much equal to populatién mean ~~ © Central Limit Theorem: When randomly sampling from any population with mean and standard deviation s, when 7 is large enough, the sampling distribution is approximately normal: ~ N(u, s/n). Usually 25, 40 to overcome extreme skewness/outliers. ©) X-bar: sample mean © Standard Exror of (X-bar) = SEC-bar) = sin Confidence Intervals ©) X-bar= t".1« SE(Y-bar) statistic —parameter © same thing as: X-bar +/- ME Standardized lest statistic: a deviation of statistic Confidence interval: statistic + (critical value) + (standard deviation of statistic) *® Fora sample of size n, the sample standard deviat Single-Sample n—1=degrees of freedom (SO much easier to ph. Put into L1. Go back into STAT > Cale > 1-Var S Statistic Danaea Deven © SEM=s/», standard error of the mean Saenen 7 T Distributions vn ul Sample Proportion [pa=p) An afin «® One-sample f statistic © [When s is known, the sampling distribution is Nm, s/V/n)] «® But whens is estimated from the sample standard deviation s, the sampling distribution follows at distribution Au, s/n) with degrees of freedom n —1 ©) When w is very large. s is avery good estimate of s, and the corresponding ¢ distributions are very close to the normal distribution ® The / distributions become wider for smaller sample sizes, reflecting the lack of precision in estimat- ing s from s. One-sample T-Confidence Intervals ©) Margin of error tt =t* sin, leading to xbar +/- the ME One-sample T-Test ® = Stating the null and alternative hypotheses (Hp versus H,) © Deciding on a one-sided or two-sided test Tf X has a binomial distribution with paramcters m and p, then: la of freedom P(X =b= (tea — py \e arve with Table T By = "Pp o, = Vipa=P) Mp =P fa _ [pd=py Vn If Z is the mean of a candom sample of size n from an infinite population with mean pt end standard deviation o, then: