MBA 604 Introduction Probaility and Statistics Lecture Notes

MBA 604 Introduction Probaility and Statistics Lecture Notes Muhammad El-Taha Department of Mathematics and Statistics University of Southern Maine 96 Falmouth Street Portland, ME 04104-9300 MBA 604, Spring 2003 MBA 604 Introduction to Probability and Statistics Course Content. Topic 1: Data Analysis Topic 2: Probability Topic 3: Random Variables and Discrete Distributions Topic 4: Continuous Probability Distributions Topic 5: Sampling Distributions Topic 6: Point and Interval Estimation Topic 7: Large Sample Estimation Topic 8: Large-Sample Tests of Hypothesis Topic 9: Inferences From Small Sample Topic 10: The Analysis of Variance Topic 11: Simple Linear Regression and Correlation Topic 12: Multiple Linear Regression 1 Contents 1 Data Analysis 5 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Graphical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Numerical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4 Percentiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5 Sample Mean and Variance For Grouped Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6 z-score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 Probability 22 1 Sample Space and Events . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2 Probability of an event . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Laws of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4 Counting Sample Points . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5 Random Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6 Modeling Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Discrete Random Variables 35 1 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2 Expected Value and Variance . . . . . . . . . . . . . . . . . . . . . . . . 37 3 Discrete Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 Markov Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4 Continuous Distributions 48 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3 Uniform: U[a,b] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4 Exponential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2 5 Sampling Distributions 56 1 The Central Limit Theorem (CLT) . . . . . . . . . . . . . . . . . . . . . 56 2 Sampling Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6 Large Sample Estimation 61 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2 Point Estimators and Their Properties . . . . . . . . . . . . . . . . . . . 62 3 Single Quantitative Population . . . . . . . . . . . . . . . . . . . . . . . 62 4 Single Binomial Population . . . . . . . . . . . . . . . . . . . . . . . . . 64 5 Two Quantitative Populations . . . . . . . . . . . . . . . . . . . . . . . . 66 6 Two Binomial Populations . . . . . . . . . . . . . . . . . . . . . . . . . . 67 7 Large-Sample Tests of Hypothesis 70 1 Elements of a Statistical Test . . . . . . . . . . . . . . . . . . . . . . . . 70 2 A Large-Sample Statistical Test . . . . . . . . . . . . . . . . . . . . . . . 71 3 Testing a Population Mean . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4 Testing a Population Proportion . . . . . . . . . . . . . . . . . . . . . . . 73 5 Comparing Two Population Means . . . . . . . . . . . . . . . . . . . . . 74 6 Comparing Two Population Proportions . . . . . . . . . . . . . . . . . . 75 7 Reporting Results of Statistical Tests: P-Value . . . . . . . . . . . . . . . 77 8 Small-Sample Tests of Hypothesis 79 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 2 Student’s t Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3 Small-Sample Inferences About a Population Mean . . . . . . . . . . . . 80 4 Small-Sample Inferences About the Difference Between Two Means: In- dependent Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5 Small-Sample Inferences About the Difference Between Two Means: Paired Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6 Inferences About a Population Variance . . . . . . . . . . . . . . . . . . 86 7 Comparing Two Population Variances . . . . . . . . . . . . . . . . . . . . 87 9 Analysis of Variance 89 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2 One Way ANOVA: Completely Randomized Experimental Design . . . . 90 3 The Randomized Block Design . . . . . . . . . . . . . . . . . . . . . . . . 93 3 10 Simple Linear Regression and Correlation 98 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2 A Simple Linear Probabilistic Model . . . . . . . . . . . . . . . . . . . . 99 3 Least Squares Prediction Equation . . . . . . . . . . . . . . . . . . . . . 100 4 Inferences Concerning the Slope . . . . . . . . . . . . . . . . . . . . . . . 103 5 Estimating E(y|x) For a Given x . . . . . . . . . . . . . . . . . . . . . . 105 6 Predicting y for a Given x . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7 Coefficient of Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 8 Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 9 Computer Printouts for Regression Analysis . . . . . . . . . . . . . . . . 107 11 Multiple Linear Regression 111 1 Introduction: Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 2 A Multiple Linear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3 Least Squares Prediction Equation . . . . . . . . . . . . . . . . . . . . . 112 4 ... - --nqh--