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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 SamFife.) 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 . lax3g "the
. '.a' ﬁn. .a'r ‘t samplmg dlrstrlbutmn 01' ? IS
appmximately a. normal. d‘istr"ibuti0n._Vi
mean (P and. standard deviation ' 635%.. Se it Weeld be. metereel .te ﬁrm a iange
sample eeefideeee' interval fer the.
pepmetieﬂ pre‘pertie e that" weeld take
the Example: A'Universitzy of: Michigan study
showed that many adults; have experienced
lingering fright from a movie or TV ShOW
they saw as a teenager. Inn4a 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: Fraporfcbn m" college student
wkie experience this
resiiuml. Maddy. The pe’im esziimemr ei‘f' ‘thie p examemf is: m" . m: ' A 983% cQﬁfidancﬁ imam1 £027 the
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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" hoped) "t0 be true, It is the
one that the 3de mustprove to be 'truu.*__e_;+ "Thus it
' requiies' Strong ' Widen6 10?? establish its. "validity. man5‘ mmmm< 
dew—n—wHg—m h}? wri‘kee Eg It often represents the current ViewPoint Or the
“status quo”. Notation: use: 3 ‘ I amaﬁve, )1 )xfafzhés €35 Paar8955; Fundamental Characteristic of a Test of Hypothesis:
Thﬂ _ Fofhﬁssis be ‘(io be, mg “£4,121 {€335 Ffﬁsenﬁg to EQL/fAeme He. rob lawmaﬂyegrfg MTE Zing; m £5 frag Test Statistic Mew LA—QS is}: a Hue #9, had 19/? 07559958. How dc. wﬁmﬁﬁsme this compatibility? , 13 nimble ‘
Th9. gyro12.0397; awn £3 6L
Vain1'2; EWWML Mare; deft“Kim (Eh ﬁg a: Vﬁimg .. The pvalue. Shows haw extreme the observed data
was, campaxed 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 slimid. 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 caagulation dismdars was placed on heparin
therapy... Oneparticular 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. (lamasing. 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. values 0f the; 12631: 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 thevalue” of a nest__statistic;
measuring. compatibility {if the data.
with the? null hypoﬂlesis. Fiﬁd the pvvalue 20f the. data, measuring
haw emfcme the data is in: the: .diirectién of the afﬁrmative hypathesisj. Compare the p:~value_'.to ' State7 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 ofthe 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
cowcc“, ilenﬁf] diHueni‘
brand. A Hypotheses:
H0: The test statistic is therefore" Peé’ Ha: F>'l5' (94‘7" I We: rajmt: 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.
 Fall '11
 Randles
 Regression Analysis

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