Statistical Theory II
Revised: November 2006
Point and interval estimation, hypothesis testing, likelihood ratio and sequential testing, correlation and regression. Prerequisite: Math 370. Three semester hours.
1. Model events occurring in nature in mathematical notation for further study.
2. Acquaint students with how to describe populations and predict events when only samples are available.
3. Illustrate how industry uses statistical models in the design and production of goods and services
4. Develop an appreciation for the use of mathematical concepts such as calculus in the development of statistics.
5. Acquaint students with the rather short history of statistics, its recent growth in applications, and current developments.
Walpole, Ronald E. Myers, Raymond H., and Myers, Sharon L. Probability and Statistics for Engineers and Scientists, Seventh Edition. Prentice-Hall, 2002.
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
- Since Chapters 1 through 6 are covered in Math 370, they should be briefly reviewed
o Chapter 1: Introduction
o Chapter 2: Probability
o Chapter 3: Random Variables and Probability Distributions
o Chapter 4: Mathematical Expectation
o Chapter 5: Some Discrete Distributions
o Chapter 6: Some Continuous Probability Distributions
- Chapter 7: Functions of Random Variables (6 days)
Introduction, Transformations of variables, Moments and moment-generating functions.
- Chapter 8: Random Sampling, Data Description, and Some Fundamental Sampling Distributions
Random sampling, Some important statistics, Data displays and graphical methods, Sampling distributions, Sampling distributions of means, Sampling distribution of S2, t-distribution, F-distribution
- Chapter 9: One and Two Sample Estimation Problems (10 days)
Statistical inference, Classical methods of estimation, Estimating the mean, Standard error of a point estimates, Tolerance limits, Estimating the difference between two means, Paired observations, Estimating a proportion, Estimating the difference between two proportions, Estimating the variance, Estimating the ratio of two variances, Bayesian methods of estimation, Maximum likelihood estimation.
- Chapter 10: One and Two Sample Tests of Hypotheses (10 days)
Statistical hypotheses, Testing a statistical hypothesis, One and two tailed tests, P-Values, Single sample tests on a single mean (variance known), Test on a mean (variance unknown), Tests on two means, Choosing sample size, Graphical methods for comparing means, Tests on a proportion, Two sample test on two proportions, One and two sample tests on variances, Goodness of fit tests, Tests of independence, Tests for homogeneity.
- Chapter 11: Simple Linear Regression and Correlation (10 days)
Introduction, Simple linear regression, Properties of the estimators, Inferences concerning the coefficients, Prediction, Choice of model, Analysis of Variance approach, Test for linearity of regression, Repeated measures, Correlation.
* Note: At appropriate places in this course, time should be allotted to elaborate on the historical aspects relevant to the subject.