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# Study Guide for Exam 1 (week 1-4 notes) STAT 200

Penn State

GPA 3.59

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## Popular in Elementary Statistics

## Popular in Statistics

This 6 page Study Guide was uploaded by Kelsey Marr on Thursday February 5, 2015. The Study Guide belongs to STAT 200 at Pennsylvania State University taught by Andrew Wiesner in Winter2015. Since its upload, it has received 1039 views. For similar materials see Elementary Statistics in Statistics at Pennsylvania State University.

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Date Created: 02/05/15

Stat 200 Wiesner Week 1amp2 Notes Basics of Statistics 0 Variable Types 0 Categorical if you d answer with a quotwordquot Binary two levels to the category 0 Ex yesno sexgender Ordinal some hierarchy or order to the levels 0 EX class standing Nominal no order or hierarchy Ex republicandemocratindependent race etc 0 Quantitative answer is a number Discrete something counted 0 Ex the number of females in class Continuous something measured 0 Ex heights of students age of students Graphing Variables o Categorical graph choices Pie chart Bar graph 0 Quantitative graph choices Histogram Stem plot Dot plot Box plot 0 Numerical Summaries 0 Measures of center Mode most frequent observation in a set of data Median middle point where about 50 of observed values in a set of data fall at or below Mean math average of all observations 0 for class discussions average will mean 0 Spread of Data 0 Range maximum minus minimum 0 Standard deviation amp variance variance SDquot2 or SD square root of variance 0 lnterquartile Range IQR third quartile minus rst quartile Data Shape o Symmetrical or bell shape O o httpcondordepauedusjostit223documentscentrahtm d 0 Right Skewed or Positively Skewed O httptheagiepiratenetaEhives403 0 Left Skewed or Negatively Skewed r39 fxffl x EXff Errf I39L FTG fine Ff O 0 mean median made 0 httpdriverlayercomimgskewed20eft20any Variance o verbal formula Take the difference between each observation and the mean These are called quotdeviationsquot We square the deviations sum them then divide by n1 0 Math expression r j Variance 5 0 Sigma summation X with line on top sample mean Xi all values of x we observe X the data Outliers 0 We can use quartiles to identify extreme observations that can be considered Outliers o A common method is to build a fence around your data Lower fence 01 15 x IQR Upper fence QB 15 x IQR Any points outside the fence are considered outliers Empirical Rule 0 A special application to data that is be shaped or approximately be shaped 0 Also known as 68 95997 Rule 0 What it means For data that is bell shaped about 68 of observations fall within one standard deviation of mean 95 of observations fall within 2 standard deviations of the mean 997 will fall within 3 standard deviations Ex heights of US adult males are approximately bell shaped with a mean of 69 inches and standard deviation of 35 inches 0 Approximately 68 of all male adults fall within heights of 69 35 in 655725 0 Approximately 95 fall within 69 7in 6276 0 Approximately 997 fall within 69 105in 585795 Zscore 0 Best used for bell shaped data 0 Gives the number of standard deviations an observation is form the mean 0 Found by Zscore observed value mean Standard deviation Stat 200 Wiesner Week 3 Notes Gathering Data 0 Three Research Strategies 0 Sample survey 0 Observational study 0 Experiment 0 Two ways to get data 0 Nonprobability methods Convenience or haphazard sample 0 Ex use our class Volunteer Ex visit website and vote in some poll 0 Probability methods Simple random sample SRS Where each subject has equal chance of being selected Strati ed random sample o The population or subjects are grouped by some distinction race class standing etc then a SRS is taken from each stratagroup Cluster sample 0 Random selection process is not one at a time but a group at a time 0 Ex randomly select a ight and interview all passengers or randomly select a section of a class and interview all students in that section The purpose of using probability methods is the use of randomness the random selection Using such techniques we gather a sample that represents some population of interest all PSU students etc Doing this then allows us to infer our sample results back to population 0 Ex if we randomly selected 1000 PSU students and 62 said campus was safe at night we can infer that 62 of all PSU students think campus is safe at night In random surveys we have a margin of error 0 Ex an error range from which the true proportion falls within 0 This margin of error can be approximated by 1square root of n where n is the sample size A common industry margin of error standard is 3 which equates to a sample size of about 1100 Bias that can appear in studiessurveys 0 Response bias subjects don t respond honestly o Nonresponse bias large percentage of sample doesn t respond 0 Selection bias we select subjects that don t represent the population of interest Observational Study 0 Where we observe subjects in their quotnatural statequot Experiments 0 Where we randomly assign some treatment Biggest difference between these two is that for an experiment we can conclude causecasual effect but for observational study only a relationship 0 In an experiment or observational study we have an explanatory variable and a responseoutcome variable Ex smoking vs lung cancer Explanatory variable smoking 0 Response variable lung cancer Ex height and weight Explanatory height 0 Response weight Blinding of subjects is done so subjects don t know what treatment they are receiving 0 Done to avoid placebo effect 0 Blind experiment researcher does not know what treatment subjects receive This is done to avoid experimenter effect 0 If both subject and experimenter are blinded we have a double blind study Stat 200 Wiesner Week 4 Notes Probability Probability o The keys Identify events Identify the probabilities to those events Ex pass Monday s exam with A B or C what is the probability to pass 0 Let P be the event you pass PP probability of passing Complement is the event of all outcomes not in the event of interest Complement to pass fail or not pass D and F 0 Rules 1 Pevent Pcomplement 1 2 O ltPA 5 1 Conditional Probability o Formulas PAB PA and BPB quotquot means the following event is given not divide Are 2 events independent 0 Yes if PA x PB PA and B 0 Decision Tree 0 Picture of the example from class tr gt w r 1 A 7 r r quot Y r r L t L Aquot 39 r M Hg I 39 39 v 39 i PHand E lm in W quot 339 Mt v A f3 k 1 h 51 39 39 is carhi I a i 1 i r L W I La 1 r I L 2 h J It r J gr 9 3 quot vu 34 v a quot v it 39Al o If you don t like the tree you can use a contingency table Win Lose Totals First Down 6 O 6 No First Down 188 212 4 Totals 788 212 10

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