In a study conducted by the Department of Health and Physical Education at Virginia Tech, 3 diets were assigned for a period of 3 days to each of 6 subjects in a randomized complete block design. The subjects, playing the role of blocks, were assigned the following 3 diets in a random order: Diet 1: mixed fat and carbohydrates, Diet 2: high fat, Diet 3: high carbohydrates. At the end of the 3-day period, each subject was put on a treadmill and the time to exhaustion, in seconds, was measured. Subject Diet 1 2 3 4 5 6 1 2 3 84 91 122 35 48 53 91 71 110 57 45 71 56 61 91 45 61 122 Perform an analysis of variance, separating out the diet, subject, and error sum of squares. Use a P-value to determine if there are significant differences among the diets, using the preceeding recorded data.

STAT-5615: Statistics in Research I Lecture 4 Probability & Probability Distributions Ott & Longnecker Chapter 4 Dr. Christian Lucero Virginia Tech Fall 2016 Introduction to Probability De▯nition A chance operation or random trial is a process or experiment that results in an outcome that cannot be predicted in advance with certainty. Example Tossing a coin, rolling a die, weighing a specimen, measuring the temperature of a patient or taking a while cell count are all examples of a chance operation. De▯nition The set of all possible outcomes of a chance operation is called a sample space for the chance operation. Example For a coin the sample space is the