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Unformatted text preview: “'qu 4.. ngeveflee. : Eg%f¥mé{£€5 C021 AQI’REE Tn'ferwde Teghé'g C3; Hypafliegégi Binary Data —when each individual observation is one of two possible outcomes. Papuk‘h’on ' ' a Suuess =0 Faéiure Population parameter : p: PFOPWfim J successes in um, Populdim, We learn about the population from a simple random sample‘ We summarize the data. via: x = a?" Santesses «in Sam-Fife.) and P ; 7%; : Pmc‘éimn§ successes in the. am pie The: Point stinloih. parameter p is: ‘ . __ W I? It is an unbiased estimator of the population proportion p. A I' _ rs: The Standard error of I When the. ;e . lax-3g "the . '.a' fin. .a'r ‘t samplmg dlrst-r-lb-u-tmn 01' ? IS appmximately a. normal. d‘i-str"ibuti0n._V-i mean (P and. standard deviation ' 635%.. Se it Weeld be. meter-eel .te firm a iange sample eeefideeee' interval fer the. pepmetiefl pre‘perti-e e that" weeld take the Example: A'Universitzy of: Michigan study showed that many adult-s; have experience-d lingering fright from a movie or TV ShOW they saw as a teenager. Inn-4a survey of 150 college students, 39 said they still experience this type of “residual anxiety” from a movie or TV Show. 111 this setting the pepulation parameter is: F: Fraporfcb-n m" college student wkie experience this resiiuml. Maddy. The pe’im esziimemr ei‘f' ‘thie p exam-emf is: m" . m: ' A 983% c-Qfifi-dancfi imam-1 £027 the I GFpuigti-n‘, paara3:21_.;eit€r is : In-tfirpm If: iii-3r: iftfi'SEI-‘V a1; ' H " ~ We» am 985 ma} in. frag, Fwy.- 53' b. I a a , _O—5 (J‘fiji‘ffl fii £3, Dada ’; (W'Ltv‘az’éy' meas; LU‘QA (1.9 0L nawkar) Po Fat, (at/"diam ngfifigfiar : jig. *3: MQQV'VL \w’! We.“ b 12.1, mag, {9591143 ) 6—1 2 Vfiivg-{aficg C Wéum (>4: ~1/CtJl‘iGLchg(L1 Void: Eéfiifi‘afl, x25 3 fl £26: 3E : gavayfq Caverga. 2* FL 2 § , - , r"; g?“ : gawk, vavmca. :—.. 3395a 731/ Cog/LJFL-émmxa lhieryaL $631,;— #1 —- S x i (20%,) 75?; (yd,ng ‘ mafia W 6:33 {&V3Q, Example: Acid rairi is a growing problem through out the US. and indeed all over the world. Forty samples of rain water are collected at a particularilocation throughout the year. Each sample is analyzed for its pH (a measure of acidity vs alkalinity) . The rain samples showed an average sample pH level of: ' '35 = [la-:7 and a sample standard deviation of s = (365” Find a 99%confidence interval for/M. , the average pH level of rain at this particular location. 0mg Tests of Hypotheses The rse‘arc‘h hypmhesis is called the an [fwflmfiv Fa .. It is Often believed (‘ '01" hope-d) "t0 be true, It is the one that the 3de mustprove to be 'truu.*__e_;+ "Thus it ' requiies' Strong ' Widen-6 10?? establish its. "validity. man-5‘- mmmm< - dew—n—w-Hg—m h}? wri‘kee Eg It often represents the current ViewPoint Or the “status quo”. Notation: use: 3- ‘ I amafive, )1 )xfafzhés €35 Paar-8955; Fundamental Characteristic of a Test of Hypothesis: Thfl _ Fofhfissis be ‘(io be, mg “£4,121- {€335 Fffisenfig to EQL/fA-eme He. rob lawmaflyegrfg MTE Zing; m £5 frag Test Statistic Mew LA—QS is}: a Hue #9, had 19/? 0755-9958. How dc. wfimfifisme this compatibility? ,- 13 nimble ‘ Th9. gyro-12.0397; awn £3 6L Vain-1'2; EWWML Mare; deft-“Kim (Eh fig a: Vfiimg .. The p-value. Shows- haw extreme the observed data was, camp-axed to the..- null ihypethesis.‘ m . that the al 1 five hypothesis true and that. the. all hypothesis is not. - (95$ Researtjhers often select a small number 9i . If [J- 3L? Ala-,2. é. 0L then they balievethat the alternativs hypothesis has been confirmed.- The numfiar o< galled the signifieance‘level of the 'test,- - . .- ‘ 7 .- _, . I r: y Mama? £L§€A. Proper Conclusions -- The mnclusien slim-id. include 'tWO 1.-The> Decision. one 01 the other): We reject :infavorof HA at ex; .=- - We fail to reject at = A {about the: Parameter of Interest: We convinced that (describe the alternative hypothesis) We arerNOT mnvinced that. (describe- the alternative hypothesis) Example: Blood caagulatien measurements were taking beme after a of patients with blood ca-agulation dismdars was placed on heparin therapy... One-particular measurement was. an. the antithrombin III Fur: each patient, What Was - recorded was: j' e change III -activity-— (after treatment level a befme treatment level)” If the. treatment was. effectiva, antithrombin. III activity should be. greater fallowing treatment and " hence these: be. 'pnsitive. If the treatment had .110 effect, than the changes should vary around 23m (basically increasing or. (lama-sing. due to. natural variation. Conduct a test of hypothesis. The parameter of intere'St in. study is; ‘" 'i w' ‘ The 111111andaliemative'hypmhesefi The test statistia in. this setting (Ankh Ha, Hal/L: has &m WPQXE e, n 1 J“ _ . .E; 31;” He 1.212% Extreme. value-s- 0f the; 1263-1: statistic in the. waif dag mime; a “:5 1175‘ _ believe. 0104 Ha). Data: _ . awllch < w, ' Steps a Test of Hypgthesis: _ 1. I Define the parameter 6f interest in. the: study. 2. State. the'nufl alternative hypotheis'es. in mi“ parameter Calculate the-value” of a nest__statistic; measuring. compatibility {if the data. with the? null hypofllesis.- Fifid the pv-value- 20f the. data, measuring haw emfcme the data is in: the: .diirectién of the affirmative hypathesisj. Compare the p:~value_-'.to ' State-7 the I Leonclusign .‘Qf the tjgst: of hYpQIhfiSiS§ Chart of congluaians and consequences: Cmdufllms a ._ ._ Reject Ha in __ favor of HA to reject Haj " In a. test of hypéthééis, the f If _ «I '1 == The level 0f Significance; .,. detemfincs: haw camPefling mug be t convince us to reject Ha Example: Can peOple tell the difference between diet coke and diet pepsi? A sample of 24 students was asked to taste test‘three cola soft drinks. They were told that two of-the three drinks were the same and the other was different. Some students had two cokes and one pepsi while others had two pepsi's and one coke. The cups were coded, but otherwise identical. Population parameter: Pg Proportion 50$ PGGP’Q. who weld cow-cc“, ilenfif] diHu-eni‘ brand. A Hypotheses: H0: The test statistic is therefore" Peé’ Ha: F>'-l5' (94‘7" I We: raj-mt: famr- pf if is; aim“. in +2 ékéreeééag. ...
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This note was uploaded on 12/10/2011 for the course STAT 4210 taught by Professor Randles during the Fall '11 term at University of Florida.

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