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Information

• Statistics is the scientific application of mathematical principles to the collection, analysis, and presentation of numerical data.

• Statisticians contribute to scientific enquiry by applying their mathematical and statistical knowledge to the design of surveys and experiments; the collection, processing, and analysis of data; and the interpretation of the results.

• Statisticians may apply their knowledge of statistical methods to a variety of subject areas, such as biology, economics, engineering, medicine, public health, psychology, marketing, education, and sports.

• Many economic, social, political, and military decisions cannot be made without statistical techniques, such as the design of experiments to gain federal approval of a newly manufactured drug.

• Statisticians provide crucial guidance in determining what information is reliable and which predictions can be trusted. They often help search for clues to the solution of a scientific mystery and sometimes keep investigators from being misled by false impressions

Course Content

Introduction and Descriptive Statistics

• Percentiles and Quartiles	• Measures of Central Tendency
• Measures of Variability	• Grouped Data and the Histogram
• Skewness and Kurtosis	• Relations between the Mean and Standard Deviation
• Methods of Displaying Data	• Exploratory Data Analysis

Probability

• Basic Definitions: Events, Sample Space, and Probabilities	• Basic Rules for Probability
• Conditional Probability	• Independence of Events
• Combinatorial Concepts	• The Law of Total Probability and Bayes’ Theorem
• Joint Probability Table

Random Variables

• Expected Values of Discrete Random Variables	• Sum and Linear Composite of Random Variables
• Bernoulli Random Variable	• The Binomial Random Variable
• The Geometric Distribution	• The Hypergeometric Distribution
• The Poisson Distribution	• Continuous Random Variables
• Uniform Distribution	• The Exponential Distribution

The Normal Distribution

• Properties of the Normal Distribution	• The Template
• The Standard Normal Distribution	• The Transformation of Normal Random Variables
• The Inverse Transformation	• The Normal Approximation of Binomial Distributions

Sampling and Sampling Distributions

• Sample Statistics as Estimators of Population Parameters	• Sampling Distributions
• Estimators and Their Properties	• Degrees of Freedom
• The Template

Confidence Intervals

• Confidence Interval for the Population Mean When the Population Standard Deviation is Known	• Confidence Intervals for m When s is Unknown - The t Distribution
• Large-Sample Confidence Intervals for the Population Proportion p	• Confidence Intervals for the Population Variance
• Sample Size Determination	• The Templates

Hypothesis Testing

• The Concept of Hypothesis Testing	• Computing the p-value
• The Hypothesis Test	• Pre-Test Decisions

The Comparison of Two Populations

• Paired-Observation Comparisons	• A Test for the Difference between Two Population Means Using Independent Random Samples
• A Large-Sample Test for the Difference between Two Population Proportions	• The F Distribution and a Test for the Equality of Two Population Variances

Analysis of Variance

• The Hypothesis Test of Analysis of Variance	• The Theory and Computations of ANOVA
• The ANOVA Table and Examples	• Further Analysis
• Models, Factors, and Designs	• Two-Way Analysis of Variance
• Blocking Designs

Simple Linear Regression and Correlation

• The Simple Linear Regression Model	• Estimation: The Method of Least Squares
• Error Variance and the Standard Errors of Regression Estimators	• Correlation
• Hypothesis Tests about the Regression Relationship	• How Good is the Regression?
• Analysis of Variance Table and an F Test of the Regression Model	• Residual Analysis and Checking for Model Inadequacies
• Use of the Regression Model for Prediction	• The Solver Method for Regression

Multiple Regression

• The k-Variable Multiple Regression Model	• The F Test of a Multiple Regression Model
• How Good is the Regression	• Tests of the Significance of Individual Regression Parameters
• Testing the Validity of the Regression Model	• Using the Multiple Regression Model for Prediction