Statistics

A Statistics course is required at the college level for completion of requirements in a surprisingly large number of fields of study that seem to vary widely. Topics in Statistics include the study of various “averages” and standard deviation and extend into probability, various sampling distributions, estimating using confidence intervals, and hypothesis testing. Special emphasis is given to real world applications. The graphing calculator is used extensively.

Table of Contents

Chapter 1 – GETTING STARTED

1.1 What Is Statistics?
1.2 Random Samples
1.3 Introduction to Experimental Design

Chapter 2 – ORGANIZING DATA

2.1 Frequency Distributions, Histograms, and Related Topics
2.2 Bar Graphs, Circle Graphs, and Time-Series Graphs
2.3 Stem-and-Leaf Displays

Chapter 3 – AVERAGES AND VARIATIONS

3.1 Measures of Central Tendency: Mode, Median, and Mean
3.2 Measures of Variation
3.3 Percentiles and Box-and-Whisker Plots

Chapter 4 – CORRELATION AND REGRESSION

4.1 Scatter Diagrams and Linear Correlation
4.2 Linear Regression and the Coefficient of Determination

Chapter 5 – ELEMENTARY PROBABILITY THEORY

5.1 What Is Probability
5.2 Some Probability Rules – Compound Events
5.3 Tree Diagrams and Counting Techniques

Chapter 6 – THE BINOMIAL PROBABILITY DISTRIBUTION AND RELATED TOPICS

6.1 Introduction to Random Variables and Probability Distributions
6.2 Binomial Probabilities
6.3 Additional Properties of the Binomial Distribution

Chapter 7 – NORMAL CURVES AND SAMPLING DISTRIBUTIONS

7.1 Graphs of Normal Probability Distributions
7.2 Standard Units and Areas Under the Standard Normal Distribution
7.3 Areas Under Any Normal Curve
7.4 Sampling Distributions
7.5 The Central Limit Theorem
7.6 Normal Approximations to the Binomial Distribution

Chapter 8 – ESTIMATION

8.1 Estimating μ When σ Is Known
8.2 Estimating μ When σ Is Unknown
8.3 Estimating p in the Binomial Distribution

Chapter 9 – HYPOTHESIS TESTING

9.1 Introduction to Statistical Tests
9.2 Testing the Mean μ
9.3 Testing a Proportion p

Chapter 10 – INFERENCES ABOUT DIFFERENCES

10.1 Tests Involving Paired Differences (Dependent Samples)
10.2 Inferences About the Difference of Two Means μ1 – μ2
10.3 Inferences About the Difference of Two Proportions p1 – p2

Chapter 11 – ADDITIONAL TOPICS USING INFERENCE

11.1 Chi-Square: Tests of Independence and of Homogeneity
11.2 Chi-Square: Goodness of Fit
11.3 Testing a Single Variance or Standard Deviation
11.4 Inferences for Correlation and Regression

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