{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

View Full Document Right Arrow Icon
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
Background image of page 1

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

View Full Document Right Arrow Icon
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
Background image of page 2
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
Background image of page 3

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

View Full Document Right Arrow Icon
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
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}