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# Introduction to Statistics I STA 2122

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This 6 page Class Notes was uploaded by Jonatan Kunde on Monday October 12, 2015. The Class Notes belongs to STA 2122 at Florida International University taught by Dongmei An in Fall. Since its upload, it has received 16 views. For similar materials see /class/221815/sta-2122-florida-international-university in Statistics at Florida International University.

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Date Created: 10/12/15

ST3123 Introduction of Statistics 11 Review A Basic Concepts in Inferential Statistics 0 Statistics descriptive statistics and inferential statistics Inferential statistics con dence interval and hypothesis test Population and Samplesimple random sample Population all subjects of interest Sample part of population Parameter u 0392 039 p and statistic f 32 s 13 Parameter descriptive measurement for population usually unknown u population mean p population proportion 62 population variance 6 population standard deviation Statistic descriptive measurement for sample known f sample mean f7 sample proportion sz sample variance 3 sample standard deviation P r 39 quot l t is quot t 39 by its con 1 39 sample statistic 0 Central Limit Theorem and sampling distribution of sample mean 1 CLT When sample size n is sufficiently large n 2 30 the sampling distribution of sample mean 9 will be approximately normally distributed with mean u u and standard dev1ation a T regardless the population distribution 11 The larger the sample size the better will be the normal approximation to the sampling distribution of 5 NO1 f y n Z f 75 3 2 1 0 1 2 2 When sample size n is small 11 lt 30 and the sample drawn from an approximately normally distributed population with mean u and population standard deviation 6 which is known 24 NO1 3 When sample size n is small n lt 30 and the sample drawn from an approximately normally distributed population with mean u and population standard deviation 0 is unknown Norma zvdislribulian rdislribution B two tables able and Mable o andard Normaltable ztable Table IV p794 1 the total area under the zcurve isL 2 mmetric and bell shaped 3 39 quot 39 z2 39 m zcurve 794 Auundlx A names TABLE w Normal Cunc Arcas Examplel Given 2 value try to find specific area under standard normal curve 1 What is P 2 gt164 Ztable gives us area A2 Symmetry about the mean tell us that A2 A1 5 P zgt 164 Al 5 7A25 4495 0505 Pz gt164 A 2 What is P z lt 164 By symmetry P z lt 164 P 2 gt164 00505 4 l 2 3 72 gl 0 1 T 2 3 64 3 What is P Z gt 196 Ztable gives us area 5 A2 4750 so A2 0250 A1 A2 4 What isPZ lt196 Symmetry about the mean tell us that A2 A1 Z P Z lt 196 00250 196 0 196 Example2 Given a specific area under standard normal curve try to find the corresponding 2 value Note Z notation 2 value which satisfiesPz 2 z a 1 What is the value of 2 that the probability 2 exceeds this value is 10 Right area a 010 then 2010 05 x f read the corresponding 2 value we get A Trytofind l 3 1 1 397 Critical Values on table Table VI p796 1 the total area under the tcurve 151 2 symmetric and bell shaped with heavy tails compared to zcurve 3 the probabilimt falls in a speci c range t t2 equals the associatedm under the t curve 4 Each tcurve is associated with its degree offreedom When the degree offreedom is getting large tcurve is close to zcurve 796 Rwandle Yams TAELLvi CriticaiannmuH m De nes of mmm Lin my hm hm 39um um rm IIellilt yrrku7ulVujmquuuwu m I ma mummun ma Examp1e3 Given a speci c area under t curve try to find the corresponding tvalue a 005 df 6 tom 1943 a0025 df15 rm 2131 a010 df8 rm 1397 0 5 t Examp1e4 Giventvalue try to find specific area under tcurve df 8 pt gt 239 toms 2306 gt pt gt 2306 0025 F t t b1 mm a 6 rm 2896 a pt gt 2896 0010 001 0 231 233 283 t So 001 lt 70 gt 239 lt 0025 Note Based on ttable we only can have the range of this area but we can use statistical software to get the exact value

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