The detailed mathematical solutions of the statistical analyses presented in this book were developed as a supplemental text for first courses in statistics. Students and practitioners involved in environmental, agricultural and biological sciences and environmental engineering with a minimal background in statistics but with a need to interpret the data gathered during their experiments will benefit most. It frequently becomes difficult to fully understand the concepts and methods presented in statistics unless detailed examples are available for review. The detailed solutions presented in this supplemental text include enough steps to insure that a student will have no difficulty in following the procedures used in the solution to the problem. All of the examples presented are based upon actual experimental results and are easily adaptable to any scientific or engineering field. The examples have been selected from a wide variety of activities in hopes that the reader will see that regardless of the subject area, the application of the statistical technique is identical. The mathematical symbols employed in this book are the same as those used by Steel and Torrie in their book, "Principles and Procedures of Statistics." These symbols were selected to provide a simple and logical method of mathematical shorthand.