{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3011CourseNotes

# 3011CourseNotes - Notes for Statistics 3011 University of...

This preview shows pages 1–5. Sign up to view the full content.

Notes for Statistics 3011 * University of Minnesota, Spring 2009 Instructor: Alicia Johnson *Notes accompany the second edition of Statistics: The Art and Science of Learning From Data by Alan Agresti and Christine Franklin

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Contents CHAPTER 1: INTRODUCTION 1 1.1 The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Role of Computers in Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Introduction to R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 Getting Started with Rweb . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.3 Entering Data in R and Rweb . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.4 Getting Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 CHAPTER 2: EXPLORING DATA 8 2.1 Types of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Graphical Summaries of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Graphical Summaries for Categorical Variables . . . . . . . . . . . . . . . . . 9 2.2.2 Graphical Summaries for Quantitative Variables . . . . . . . . . . . . . . . . 12 2.3 Numerical Summaries of Quantitative Data . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.1 Measures of Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.2 Measures of Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 CHAPTER 5: PROBABILITY 31 5.1 Randomness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.2 Probability Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.3 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 CHAPTER 6: PROBABILITY DISTRIBUTIONS 50 6.1 Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6.1.1 Probability Distribution of a Discrete Random Variable . . . . . . . . . . . . 51 6.1.2 Center and Spread of a Probability Distribution . . . . . . . . . . . . . . . . 53 6.2 Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6.2.1 Density Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6.2.2 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.2.3 The Normal Distribution in R . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 6.3 The Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 CHAPTER 7: SAMPLING DISTRIBUTIONS 82 7.1 The Sampling Distribution of a Sample Mean . . . . . . . . . . . . . . . . . . . . . . 85 7.2 The Sampling Distribution of a Sample Proportion . . . . . . . . . . . . . . . . . . . 90
Stat 3011 Chapter 0 CHAPTER 8: CONFIDENCE INTERVALS 94 8.1 Point Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 8.2 Interval Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 8.2.1 Confidence Intervals for a Population Proportion, p . . . . . . . . . . . . . . . 97 8.2.2 Confidence Intervals for a Population Mean, μ . . . . . . . . . . . . . . . . . 107 CHAPTER 9: HYPOTHESIS TESTS 115 9.1 Elements of a Hypothesis Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 9.2 Hypothesis Tests for Population Proportion p . . . . . . . . . . . . . . . . . . . . . . 120 9.3 The t -Test: Hypothesis Testing for Population Mean μ . . . . . . . . . . . . . . . . . 124 9.4 Possible Errors in Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 129 9.5 Limitations and Common Misinterpretations of Hypothesis Testing . . . . . . . . . . 131 CHAPTER 10: COMPARING TWO GROUPS 133 10.1 Comparing Two Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 10.1.1 Point Estimation for p 1 - p 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 10.1.2 Confidence Intervals for p 1 - p 2 . . . . . . . . . . . . . . . . . . . . . . . . . 134 10.1.3 Hypothesis Tests for Comparing p 1 and p 2 . . . . . . . . . . . . . . . . . . . 136 10.2 Comparing Two Means - Matched Pairs . . . . . . . . . . . . . . . . . . . . . . . . 140 10.3 Comparing Two Means - Independent Populations . . . . . . . . . . . . . . . . . . 143 10.3.1 Point Estimation for μ 1 - μ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 10.3.2 Confidence Intervals for μ 1 - μ 2 . . . . . . . . . . . . . . . . . . . . . . . . . 145 10.3.3 The Two-Sample t -Test for Comparing μ 1 and μ 2 . . . . . . . . . . . . . . . 145 CHAPTER 3: 2-VARIABLE ASSOCIATIONS 152 CHAPTER 11: ASSOCIATION BETWEEN TWO CATEGORICAL VARIABLES154 11.1 Chi-Squared Test for Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 11.2 Measures of Association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 CHAPTER 12: REGRESSION ANALYSIS 164 12.0 Exploring the Data (A Return to Chapter 3) . . . . . . . . . . . . . . . . . . . . . . 165 3.2.1 Graphical Summaries - The Scatterplot . . . . . . . . . . . . . . . . . . . . . 165 3.2.2 Numerical Summaries - Correlation . . . . . . . . . . . . . . . . . . . . . . . . 168 3.2.3 Numerical Summaries - Least Squares Regression . . . . . . . . . . . . . . . . 171 12.1 Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 12.2 Inference About the Population Regression Model . . . . . . . . . . . . . . . . . . . 181 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
12.1.1 Estimating α and β . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 12.1.2 Hypothesis Tests and Confidence Intervals for β . . . . . . . . . . . . . . . . 183 12.1.3 Measuring the Strength of the Linear Relationship . . . . . . . . . . . . . . 185 12.3 Checking the Model Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 12.4 Correlation and Regression: A Cautionary Tale . . . . . . . . . . . . . . . . . . . . 190 CHAPTER 13: MULTIPLE REGRESSION 195 13.1 The Multiple Regression Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 13.2 Estimation of the Multiple Regression Model . . . . . . . . . . . . . . . . . . . . . . 197 13.3 Inference for the Multiple Regression Model . . . . . . . . . . . . . . . . . . . . . . 200 CHAPTER 14: ANALYSIS OF VARIANCE 208 14.1 One-Way ANOVA
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}