Chapter 1 Sampling and Data R K Sahi Austin Peay State University sahir apsu edu R K Sahi APSU Ch 1 Introduction 1 34 Overview 1 What Is Are Statistics 2 Goal 3 Key Terms of Statistical Studies 4 Measures of Data R K Sahi APSU Ch 1 Introduction 2 34 What Is Are Statistics Statistics is the art and science of learning from data This involves determining research questions planning data collection for the study collecting the data cleaning the data analyzing the data interpreting the analysis and presenting the ndings Example 1 The average amount of TV watched per day 2 The percentage of people who are concerned about global warming 3 The median height of women in college 4 The range of handspans for college statistics students R K Sahi APSU Ch 1 Introduction 3 34 Main Components of Statistics There are three main components of statistics for answering a statistical question 1 Design Planning how to obtain data You can use survey which are readily available on Internet General Social Survey or you can create your own by looking at what population you are looking at for example APSU students or TN or USA R K Sahi APSU Ch 1 Introduction 4 34 Main Components of Statistics cont 2 Description Summarizing the data obtained 1 It involves gathering organizing and summarizing data graphs charts tables averages standard deviations percentiles maximums etc 2 You can do that by creating graphical displays such as histograms piecharts etc R K Sahi APSU Ch 1 Introduction 5 34 Main Components of Statistics cont 3 Inference Making decisions and predictions using probability and probability distributions Does too much of TV watching a ects students grades or GPA What are the e ects of global warming over the past decade R K Sahi APSU Ch 1 Introduction 6 34 Practice Problems 1 2 3 Inferential or descriptive There were 26 con rmed cases of West Nile virus in Tennessee in 2003 Inferential or descriptive From past gures it is predicted that 47 of the registered voters in Virginia will vote in the June primary Inferential or descriptive In October 2002 ABCNews com reported 73 of Americans favor a law requiring all guns sold in the US be test red rst so law enforcement would have ballistic ngerprints in case a rearm is used in a crime R K Sahi APSU Ch 1 Introduction 7 34 Goal of Statistics 1 Goal of Statistics is not to perform numerous calculations using the formulas but to gain an understanding of your data 2 The calculations can be done using a calculator or a computer The understanding must come from you 3 If you can thoroughly grasp the basics of statistics you can be more con dent in the decisions you make in life R K Sahi APSU Ch 1 Introduction 8 34 Key Terms Population and Sample In a statistical research the entities that we measure in a study are called subjects These subjects may re ect all the entities or a part of it Population All subjects of interest You can think of a population as a collection of persons things or objects under study Sample is portion subset of the population To study the population we select a sample The idea of sampling is to select a portion of the larger population and study that portion the sample to gain information about the population R K Sahi APSU Ch 1 Introduction 9 34 Practice Problems 1 To predict the outcome of the 2010 gubernatorial election in California an exit poll sampled 3889 of the 9 5 million people who voted De ne the sample and the population for this exit poll 2 In a UW Madison study 100 of the 40 858 student body members were asked On how many days in the past week did you consume at least one alcoholic drink Identify the population and the sample R K Sahi APSU Ch 1 Introduction 10 34 Practice Problems 1 We want to know the average mean amount of money rst year college students spend at San Jose College SJC on school supplies that do not include books We randomly survey 100 rst year students at the college Three of those students spent 150 200 and 225 respectively Determine the population and sample The population is all rst year students attending SJC who spent money on school supplies excluding books The sample is the 100 rst year students at the SJC who spent money on school supplies excluding books R K Sahi APSU Ch 1 Introduction 11 34 Key Terms Parameter and Statistic A Parameter is a numerical summary of the population Example Proportion of all teenagers in the United States who have smoked in the last month A Statistic is a numerical summary of a sample taken from the population Example Proportion of teenagers who have smoked in the last month out of a sample of 200 randomly selected teenagers in the United States R K Sahi APSU Ch 1 Introduction 12 34 Practice Problems Example We want to know the average mean amount of money rst year college students spend at San Jose College on school supplies that do not include books We randomly survey 100 rst year students at the college Three of those students spent 150 200 and 225 respectively Determine the parameter population and statistics sample R K Sahi APSU Ch 1 Introduction 13 34 Practice Problems Example In a UW Madison study 100 of the 40 858 student body members were asked On how many days in the past week did you consume at least one alcoholic drink Also one parameter of interest is the proportion of the student body that would respond zero to this question Suppose 29 of those who were sampled gave this response Is the numerical survey of 29 a statistic sample or a parameter population R K Sahi APSU Ch 1 Introduction 14 34 Key Term Variable Variable A variable notated by capital letters such as X and Y is a characteristic of interest for each person or thing in a population or sample Example Determine the variable We want to know the average mean amount of money rst year college students spend at San Jose College on school supplies that do not include books We randomly survey 100 rst year students at the college Three of those students spent 150 200 and 225 respectively The variable could be the amount of money spent excluding books by one rst year student Let X the amount of money spent excluding books by one rst year student attending San Jose College R K Sahi APSU Ch 1 Introduction 15 34 Key Term Variable cont Variables may be numerical or categorical Numerical variables take on values with equal units such as weight in pounds and time in hours Categorical variables place the person or thing into a category Example 1 2 If we let X equal the number of points earned by one math student