PSTAT 5A List of topics

Transcription

1 PSTAT 5A List of topics 1 Introduction to Probability 2 Discrete Probability Distributions including the Binomial Distribution 3 Continuous Probability Distributions including the Normal Distribution 4 Collecting, Describing and Summarizing Data 5 Sampling Distributions 6 Inference about Population Proportions 7 Inference about One Population Mean 8 Inference about Two Population Means 9 Correlation and Linear Regression 10 Introduction to Multiple Regression Analysis 11 Inference for Regression 12 Bayesian Statistics (if time allows)

2 DETAILED TABLE OF CONTENTS 1 What is Statistics? 1.1 What will I learn? 1.2 Why do I need to study statistics? 1.3 What do I already know that will help me to understand statistics? 1.4 Thinking critically about statistics. 2 Introduction to Probability 2.1 Introduction. 2.2 Sample spaces. 2.3 Some basic rules of probability. 2.4 Mutually exclusive events. 2.5 Independent events. 2.6 Introduction to Excel 2.7 Summary 2.8 Formulas 2.9 Exercises What can I do with this? 3 Discrete Random Variables and their Probability Distributions 3.1 Introduction. 3.2 Probability distributions. 3.3 Mean, variance and expectation 3.4 Counting rules 3.5 Binomial distribution. 3.6 Poisson distribution 3.7 Excel 3.8 Summary 3.9 Formulas 3.10 Exercises 3.11 What can I do with this? 4 Continuous Random Variables and their Probability Distributions 4.1 Introduction. 4.2 Uniform distribution 4.3 Standard Normal distribution 4.4 Normal distribution 4.5 Excel 4.6 Summary

3 4.7 Formulas 4.8 Exercises 4.9 What can I do with this? 5 Describing and Exploring Data 5.1 Introduction. 5.2 Graphical summaries 5.3 Numerical summaries 5.4 Sampling methods 5.5 Excel 5.6 Summary 5.7 Formulas 5.8 Exercises 5.9 What can I do with this? 6 Sampling Distributions 6.1 Introduction. 6.2 The law of large numbers 6.3 The central limit theorem 6.4 Normal approximation to the binomial 6.5 Excel 6.6 Summary 6.7 Formulas 6.8 Exercises 6.9 What can I do with this? 7 Inference about Population Proportions 7.1 Probability, statistics and inference: confidence intervals and hypothesis tests 7.2 Confidence interval for a population proportion 7.3 Hypothesis test for a population proportion 7.4 Confidence interval for the difference between two population proportions 7.5 Hypothesis test for the difference between two population proportions 7.6 Excel 7.7 Summary 7.8 Formulas 7.9 Exercises 7.10 What can I do with this?

4 8 Inference about a Single Population Mean 8.1 Introduction. 8.2 Confidence interval for a mean when σ is known 8.3 Hypothesis test for a mean when σ is known 8.4 Confidence interval for a mean when σ is unknown 8.5 Hypothesis test for a mean when σ is unknown 8.6 Excel 8.7 Summary 8.8 Formulas 8.9 Exercises 8.10 What can I do with this? 9 Inference about Two Population Means 9.1 Confidence interval for the difference between two means: independent samples σ1 and σ2 known 9.2 Hypothesis test for two means: independent samples σ1 and σ2 known 9.3 Confidence interval for the difference between two means: independent samples σ1 and σ2 unknown 9.4 Hypothesis test for two means: independent samples σ1 and σ2 unknown 9.5 Confidence interval for two dependent samples (matched pairs) 9.6 Hypothesis test for two dependent samples (matched pairs) 9.7 Excel 9.8 Summary 9.9 Formulas 9.10 Exercises 9.11 What can I do with this? 10 Correlation and Linear Regression 11.1 Introduction 11.2 Scatterplots 11.3 Coefficient of correlation 11.4 Least Squares line of best fit 11.5 Coefficient of determination 11.6 Excel 11.7 Summary 11.8 Formulas 11.9 Exercises What can I do with this? 11 Multiple Regression Analysis

5 11.1 Introduction 11.2 Multiple regression model 11.3 Least Squares method 11.4 Multiple coefficients of determination 11.5 Excel 11.6 Summary 11.7 Formulas 11.8 Exercises 11.9 What can I do with this? 12 Inference for Regression 12.1 Introduction 12.2 Testing for Significance: t test and F-test linear 12.3 Testing for Significance: t test and F-test non-linear 12.4 Using Excel s regression tool 12.5 Estimation and predication using Excel 12.6 Summary 12.7 Formulas 12.8 Exercises 12.9 What can I do with this? Tables Solutions to odd-numbered exercises Index