Mathematics Department Indiana University of Pennsylvania Indiana, PA 15705 Course Number: MA 216 Course Title: Probability and Statistics for Natural Sciences Credits: 4 semester hours Prerequisites: MA 121, or 123, or 127 Textbook: Introduction to the Practice of Statistics Moore Freeman Revised: 9/94 Catalog Description:Frequency distributions, measures of central tendency and variation, probability, probability distributions, sampling distributions. Hypothesis testing for means, variances, proportions. Correlation, regression, analysis of variance, and nonparametric statistics. Emphasis on applications. The computer is used for data analysis.
Course Outline I. Looking at Data: Distributions A. Displaying Distributions 1. Measurement 2. Variation 3. Stemplots 4. Histograms 5. Looking at Data 6. Time Plots B. Describing Distributions 1. Measuring Center 2. Resistant Measures of Spread 3. The Standard Deviation 4. Changing the Unit of Measurement C. The Normal Distributions 1. Density Curves 2. Normal Distributions 3. Normal Distribution Calculations 4. Assessing Normality II. Looking at Data: Relationships A. Scatterplots 1. Interpreting Scatterplots 2. Smoothing Scatterplots 3. Categorical Explanatory Variables B. Least Squares Regression 1. Fitting a Line to Data 2. Least-Squares Regression 3. Residuals 4. Outliers and Influential Observations C. Correlation 1. Computing the Correlation 2. Correlation in the Regression Setting 3. Interpreting Correlation and Regression D. Relations in Categorical Data 1. Analyzing Two-Way Tables 2. Simpson's Paradox E. The Question of Causation 1. Smoking and Lung Cancer 2. Establishing Causation III. Producing Data A. First Steps 1. The Need for Design 2. Sampling 3. Experiments B. Design of Experiments 1. Comparative Experiments 2. Randomization 3. How to Randomize 4. Cautions about Experimentation 5. Other Experimental Designs C. Sampling Design 1. Simple Random Samples 2. Other Sampling Designs 3. Cautions about Sample Surveys D. Toward Statistical Inference 1. Sampling Distributions 2. Bias 3. Variability 4. What about Experiments? 5. Conclusion IV. Probability: The Study of Randomness A. Probability Models 1. Sample Spaces 2. Assigning Probabilities 3. Addition and Multiplication Rules B. Random Variables 1. Discrete Random Variables 2. Continuous Random Variables C. Means and Variances of Random Variables 1. The Mean of a Random Variable 2. The Law of Large Numbers 3. Rules for Means 4. The Variance of a Random Variable 5. Rules for Variances D. Probability Laws 1. General Addition Rules 2. Conditional Probabilities and General Multiplication Rules V. From Probability to Inference A. Counts and Proportions 1. The Binomial Distributions 2. Binomial Probabilities 3. Binomial Mean and Variance 4. Sample Proportions 5. Normal Approximation for Proportions and Counts B. Sample Means 1. The Distribution of a Sample Mean 2. The Central Limit Theorem C. Control Charts 1. Control Charts 2. Out-of-Control Signals VI. Introduction to Inference A. Estimating with Confidence 1. Statistical Confidence 2. Confidence Intervals 3. How Confidence Intervals Behave B. Tests of Significance 1. The Nature of Significance Testing 2. Tests for a Population Mean 3. Tests with Fixed Significance Level C. Use and Abuse of Tests 1. Using Significance Tests 2. Abuse of Significance Tests 3. Power 4. Inference As Decision VII. Inference for Distributions A. Inference for the Mean of a Population 1. The One-Sample t Procedures 2. Matched Pairs t Procedures 3. The Power of the t Test 4. Inference for Nonnormal Populations B. Comparing Two Means 1. The Two-Sample z Statistic 2. The Two-Sample t Procedures 3. The Pooled Two-Sample t Procedures VIII. Inference for Count Data A. Inference for a Single Proportion 1. Confidence Intervals and Significance Tests 2. Choosing A Sample Size B. Comparing Two Proportions 1. Confidence Intervals 2. Significance Tests C. Inference for Two-Way Tables 1. Describing Relations in Two-Way Tables 2. The Chi-Square Test 3. Computations 4. Models for Two-Way Tables IX. Inference for Regression A. Simple Linear Regression 1. Statistical Model For Linear Regression 2. Estimating the Regression Parameters 3. Confidence Intervals and Significance Tests 4. Confidence Intervals For Mean Response 5. Prediction Intervals 6. Analysis of Variance For Regression 7. Calculations for Regression Inference 8. Inference for Correlation X. Analysis of Variance A. One-Way Analysis of Variance 1. Comparing Means 2. The ANOVA Model 3. The ANOVA Table and the F Test 4. Multiple Comparisons Supplemental Materials: Telecourse Study Guide for Against All Odds and Introduction to the Practice of Statistics Author: Moore Publisher: Freeman Minitab Guide: Introduction to the Practice of Statistics Author: Greenberg Publisher: Freeman STAT 101 Author: Addison-Wesley Publisher: Addison-Wesley
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