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# Week 4 Notes Math 243

UO

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This 4 page Class Notes was uploaded by Elizabeth Notetaker on Sunday April 26, 2015. The Class Notes belongs to Math 243 at University of Oregon taught by Price in Spring2015. Since its upload, it has received 143 views.

## Reviews for Week 4 Notes

Better than the professor's notes. I could actually understand what the heck was going on. Will be back for help in this class.

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Date Created: 04/26/15

Aldpter Sampling DiSfI iblltitnm Mgm Sm 39I Def 4L 39 7 r w MMMMWJ pamnwur 1S 1 variable 3 1quot 7 A 3 qu E 111113 to the populatlun usually uriknnwn la 1 mnable pertmning to the 1 39 2 V V E 1 T k mnnp Ligually used to F LjIll i o m unlmnwn 111211116 11 1 x 1e nwan net v 39 39 uf 100 11011591 Eamon Wages for Indwuiuals in the United Stairs was 113 1311351 A WWWquot the Emmi Sm 1 wand 3 1119311 Income of 46 091 The mpde not mmlpusujltm for imliviehmlrs in t 11119 as 33803102 711911 studying the Unitvd Stains whth values am Immm quotquot5 and whichme statistics teem veg PoPu ga TM I 39 7 quot a 4100 a gms c omw album sun 15 4 20393t02 PW cm Y c Uwgt populi quot 39 g rquot 39 5 1 m A group of mlddle school students n xeasures the helght of dandchons m a large eld The 311151011 are divided into four groups containing ve students each and each student l39nmjmms the height quot1 cm of one dandelion chosen at random We assume that these heights are frmn a Normal distributlml with unknown mean p Group 1 137 153 91 160 161 Group 2 139 95 127 169 135 Group 3 173 108 177 118 217 Group 4 132 134 201 158 162 What is the sample mean 13 for the rst group s observations What iquot for the rst ter gmUPS together The rst three together All four groups together yWUv X 3 31153 qJ t l39v i39 UL 214 an be 2739 X 31311597 CW 0 I mast h imp 1132 44 um PJF Y s mmm 2 r M dy 5 314733 M at Iumbers states that as the number of observations increases the 11102111 31 the Def 1 The Law of Lara r I K 7 sample 2 approaches the true 111931 of the populatmn u M sawu We 1 i y p 118 Mzmxpf Chaptpr 1 Sampling Ulhtl mm 7 wwmwwwWMmA I mnly Ex 3 Using the d 7i quotm imlr39pvml am wt In Eamnmlc 392 m zlcul1t mush lm1P5quot 5 11 1 1 I 3 E 53140 bW39vpl If339g 9W3LS 13 09 OWW sr HSf H Th san lpling digtrilmtiun of a stalisiic is tht listrilmtjnn uf uhsurnnierm Whm w mkv all numb sgmlplm if a nal size from the Impulntiun 813 dbm b h 6E an I j djV gnu p 1m The sampling distrll39n mu of A 1115 1116311 11 and smndanl dvvmmn 7 19 1mg A thew mnn ms an 39 391 u 39 39 39 SRSS of 5122 n tbtmnmi fmm a pupulamm With tman p and standard lvvmticm n Furthvrmnrm thv sampling distrilmtiml 0139 Y is ixax39tly Normal if the t iisatribmiun uf i ffr iitiiii39l X is Mama The distrilmtiml m X a rmuim n ohsnrvatiun and the distrihmiun uf X a mmlmn munpiv 11mm an dim rent Th9 have the same mum but tho distributim m uf X has 111th hm mriminm Hum X J 1 my 11 ml A swam Note 9 i m I 1 ff TN J My 33 r m ewwrf a fa phi 1amp1 r w A 1145 N529 5quot 39 39 39 WWHW A Chapter firA a 1ku a s un t uf 4 dad dy y n x a Uhtx 11 Sampling Dis mu 39tt lb xILiOHS 1243 Sm quot915 395 39 us with d r r r M La i v Ex 1 mm 3quot hurinal dwtr mtim havng mean 45 and stun a q 13 1135111 39 9 mum in 1 33 0 my him 1 tan A 1 31 th 31 IS a DIMEability lt an ID Served V1111 c What is the prolml39ility that the DhSCI39VPd sample ram the pupul iio is mean is greater than 639 h g 17631 er than 6 1N Pb 7L0 3 MNQ VCX7 gdf fgilmiaxs 39 YWNWCAQ twol lgfggt c Pillowquot STEM C 39 k 7 em a v 39 m u r a r I f1 Lmux Theorem The sanmhng dist ributien of X is appmmmately N M an regardless of the that ribm u m a Rornu ity by writing 53 m V r 39 of the pupu la tion as lung 35 we use a large enough SRS W e express approximate X quot 4 ya in Ex 5 Let X be a randmnly selected US person s net cmnpeusation 23 studied in Example 1 remember that income is usually very Skiermedtg not ormal aquot EhaIr is the mean of the distribution for b Asaume that we know the standard de X 1 a rantium sample of 8 US adults Tm t 533 m viaion of the distribution for X is a l39 l r Iv a VWL 7C a quot mx 18 200 Vhat is the Standard deviation of the distribution for X 3 I 39 r 5 M quota 393 M 3 E wm 1 a ram Lij J i LC r n Fquot My a v e v39 g mm H It Ulmplvr 11 w Minimum lHII jilhnlln h W I HI39I WUW H mnnph39 t39 haul m 3 r 7 r I V A I Hm Hill rmnlmu 3mm 1 V WW mm um I 39 new Hui Mamimd hwlm rhwf39 mil39w 39 H j 1 l 11 In f NIH whnt m flu ppmmum Hm I m r I I w W M I I H WWW Hump mm Hm uf thv mmph 11mm in hull m lvm Hum firstmmng GM 397 5m m 1W f z I 5 E FI ow I 39 z 5quot 1 i I i y r quot f f 5 I r g I a i V I 5 4 u I Lari 9 quot I 7 f p i 39 9 P I 3 f t 39j39y i if 3i 3 f 15 i f 1 L b3 7 13 E at Lisa gf ali a l39 tiff V 1 l 1 A nk iii f if I if I Vijayijx r l quotX i I w r w x Mid 5 5 W J Li39 IT39S 739 E11 I va l 39is 139 f x 7quot H CINE 3 J 3 a t 39f A39 M g 1 W13 f r I 7 r x 39 a gt i a39 V Kw FH I In 2 v m quot N n39 39 39 39 Aquot I i quot a P 1 5 5171 a C 39139 C 39 a a z m z w 3 2 7 b i H x I 39 I Y H F332 3 LN I Iu39 rsmclum vminMv F1 t r mrt 111v lmmht39rj Hf ms fmmd m 1 gnu n lmum hull dug Nah HI til ihilliml jmx t Numml it isn39t Wn at c rml immus disttiihutinn Himv wn mm only lmw39 n whnlv uumv r H v 1 v ztim lwr nf Imus Hm mpululmn mm mm Ianmulls ymxrn lh lewn ten In 7 wth t uni mi ti H I 7 MM 1 What irs thenppmxinmlxpmhnhilily21mm h Im39nlvnlntn thv prulmhiliiy from part it mminm sample 1149 er 3 will lmw a mmm with a szrnplv Hizv of lliHIL UT munquot Hum 3 was m 1 a h if F r i k 7 j gt C 7 7 39quotVUY W149 1725 21 3mm 7 1 1 rim L mmr J 2 f gt hi w Qtquot if t A mwwmmo A 131 AW a v a iv 391 a mmqu raj

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