Brief Introduction To Probability And Statistics - With Cd - 02 edition

1. DESCRIBING DATA WITH GRAPHS.

Variables and Data.
Types of Variables.
Graphs for Categorical Data.
Graphs for Quantitative Data.
Relative Frequency Histograms.

2. DESCRIBING DATA WITH NUMERICAL MEASURES.

Describing a Set of Data with Numerical Measures.
Measures of Center.
Measures of Variability.
On the Practical Significance of the Standard Deviation.
A Check on the Calculation of s.
Measures of Relative Standing.
The Box Plot.

3. DESCRIBING BIVARIATE DATA.

Bivariate Data.
Graphs for Qualitative Variables.
Scatterplots for Two Quantitative Variables.
Numerical Measures for Quantitative Bivariate Data.

4. PROBABILITY AND PROBABILITY DISTRIBUTIONS.

The Role of Probability in Statistics.
Events and the Sample Space.
Calculating Probabilities Using Simple Events.
Useful Counting Rules (Optional).
Event Composition and Event Relations.
Conditional Probability and Independence.
Bayes' Rule (Optional).
Discrete Random Variables and Their Probability Distributions.

5. SEVERAL USEFUL DISCRETE DISTRIBUTIONS.

Introduction.
The Binomial Probability Distribution.
The Poisson Probability Distribution.
The Hypergeometric Probability Distribution.

6. THE NORMAL PROBABILITY DISTRIBUTION.

Probability Distributions for Continuous Random Variables.
The Normal Probability Distribution.
Tabulated Areas of the Normal Probability Distribution.
The Normal Approximation to the Binomial Probability Distribution (Optional).

7. SAMPLING DISTRIBUTIONS.

Introduction.
Sampling Plans and Experimental Designs.
Statistics and Sampling Distributions.
The Central Limit Theorem.
The Sampling Distribution of the Sample Error.
The Sampling Distribution of the Sample Proportion.
A Sampling Application: Statistical Process Control (Optional).

8. LARGE-SAMPLE ESTIMATION.

Where You've Been.
Where You're Going Statistical Inference.
Types of Estimators.
Point Estimation.
Interval Estimation.
Estimating the Difference Between Two Population Means.
Estimating the Difference Between Two Binomial Proportions.
One-Sided Confidence Bounds.
Choosing the Sample Size.

9. LARGE-SAMPLE TESTS OF HYPOTHESES.

Testing Hypotheses About Population Parameters.
A Statistical Test of Hypothesis.
A Large-Sample Test About a Population Mean.
A Large-Sample Test of Hypothesis for the Difference Between Two Population Means.
A Large-Sample Test of Hypothesis for a Binomial Proportion.
A Large-Sample Test of Hypothesis for the Difference Between Two Binomial Proportions.
Some Comments on Testing Hypotheses.

10. INFERENCE FROM SMALL SAMPLES.

Introduction.
Student's t Distribution.
Small-Sample Inferences Concerning a Population Mean.
Small-Sample Inferences for the Difference Between Two Population Means: Independent Random Samples.
Small-Sample Inferences for the Difference Between Two Means: A Paired-Difference Test.
Inferences Concerning a Population Variance.
Comparing Two Population Variances.
Revisiting the Small-Sample Assumption.

11. THE ANALYSIS OF VARIANCE.

The Design of an Experiment.
What is an Analysis of Variance?
The Assumptions for an Analysis of Variance.
The Completely Randomized Design: A One-Way Classification.
The Analysis of Variance for a Completely Randomized Design.
Ranking Population Means.
Revisiting the Analysis of Variance Assumptions.
A Brief Summary.

12. LINEAR REGRESSION AND CORRELATION.

Introduction.
A Simple Linear Probabilistic Model.
The Method of Least Squares.
An Analysis of Variance for Linear Regression.
Testing the Usefulness of the Linear Regression Model.
Estimation and Prediction Using the Fitted Line.
Revisiting the Regression Assumptions.
Correlation Analysis.

13. ANALYSIS OF CATEGORICAL DATA.

A Description of the Experiment.
Pearson's Chi-Square Statistic.
Testing Specified Cell Probabilities: The Goodness-of-Fit Test.
Contingency Tables: A Two-Way Classification.
Comparing Several Multinomial Populations: A Two-Way Classification with Fixed Row or Column Totals.
The Equivalence of Statistical Tests.
Other Applications of the Chi-Square Test.

APPENDIX: TABLES.

Cumulative Binomial Probabilities.
Cumulative Poisson Probabilities.
Normal Curve Areas.
Critical Values of t.
Critical Values of Chi-Square.
Percentage Points of the F Distribution.
Random Numbers.
Percentage Points of the Studentized Range, q(k, df).

ANSWERS TO SELECTED EXERCISES.
INDEX.