Approved 2/3/2014 Departmental Syllabus Math 4030 – Statistical Methods with Applications Textbook: Applied Statistics and Probability for Engineers, 6th ed., Montgomery & Runger, 2014 Prerequisites: MATH 2740 with a grade of “C-” or better Calculators: A scientific calculator (such as one of the TI-30 models) or a graphing calculator (such as the TI-83, 84, 85, 86 or the TI-Nspire with TI-84 keypad) is required. Calculators with Computer Algebra Systems (CAS), (e.g. the TI-89, TI-92 and TI-Nspire with CAS keypad, or their equivalent), are not allowed in any math classes. On occasion, individual instructors may restrict the use of any type of calculator. Course Description: Introduction to probability, density and distribution functions, special discrete and continuous distributions, estimation, hypothesis testing, chi-square, correlation and regression. Topics and sections to be covered: Chapter 1: The Role of Statistics in Engineering 1.1 The Engineering Method and Statistical Thinking 1.2 Collecting Engineering Data 1.3 Mechanics and Empirical Models 1.4 Probability and Probability Models Chapter 2: Probability 2.1 Sample Spaces and Events 2.2 Interpretations and Axioms of Probability 2.3 Addition Rules 2.4 Conditional Probability 2.5 Multiplication and Total Probability Rules 2.6 Independence 2.7 Bayes’ Theorem 2.8 Random Variables Chapter 3: Discrete Random Variables and Probability Distributions 3.1 Discrete Random Variables 3.2 Probability Distributions and Probability Mass Functions 3.3 Cumulative Distribution Functions 3.4 Mean and Variance of a Discrete Random Variable 3.5 Discrete Uniform Distribution 3.6 Binomial Distribution 3.7 Geometric and Negative Binomial Distributions 3.8 Hypergeometric Distribution 3.9 Poisson Distribution Chapter 4: Continuous Random Variables and Probability Distributions 4.1 Continuous Random Variables 4.2 Probability Distributions and Probability Density Functions 4.3 Cumulative Distribution Functions 4.4 Mean and Variance of a Continuous Random Variable 4.5 Continuous Uniform Distribution 4.6 Normal Distribution 4.7 Normal Approximation to the Binomial and Poisson Distributions (optional) 4.8 Exponential Distribution Approved 2/3/2014 4.9 4.10 4.11 Erlang and Gamma Distributions (optional except for Gamma Function) Weibull Distribution Lognormal Distribution (optional) Chapter 6: Descriptive Statistics 6.1 Numerical Summaries of Data 6.2 Stem-and-Leaf Diagrams 6.3 Frequency Distributions and Histograms 6.4 Box Plots 6.5 Time Sequence Plots 6.6 Scatter Diagrams 6.7 Probability Plots Chapter 7: Point Estimation of Parameters and Sampling Distributions 7.1 Point Estimation 7.2 Sampling Distributions Chapter 8: Statistical Intervals for a Single Sample 8.1 Confidence Interval on the Mean of a Normal Distribution, Variance Known 8.2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown 8.3 Confidence Interval on the Variance and Standard Deviation of a Normal Distribution 8.4 Large-Sample Confidence Interval for a Population Proportion 8.7 Tolerance and Prediction Intervals Chapter 9: Tests of Hypotheses for a Single Sample 9.1 Hypothesis Testing 9.2 Tests on the Mean of a Normal Distribution, Variance Known 9.3 Tests on the Mean of a Normal Distribution, Variance Unknown 9.4 Tests on the Variance and Standard Deviation of a Normal Distribution 9.5 Tests on a Population Proportion 9.7 Testing for Goodness of Fit 9.8 Contingency Table Tests Chapter 10: Statistical Inference for Two Samples 10.1 Inference on the Difference in Means of Two Normal Distributions, Variances Known 10.2 Inference on the Difference in Means of Two Normal Distributions, Variances Unknown 10.4 Paired t-Test 10.5 Inference on the Variances of Two Normal Distributions 10.6 Inference on Two Population Proportions Chapter 11: Simple Linear Regression and Correlation 11.1 Empirical Models 11.2 Simple Linear Regression 11.8 Correlation If you require an accommodation due to a disability, please make an appointment to see me as soon as possible to discuss arrangements for the accommodations. You will need a Verified Individualized Services and Accommodations (VISA) form from Services for Students with Disabilities.