1. What important assumption about the relation between blocks and treat- ments is necessary for carrying out a block design ANOVA?

2. Public concern has recently focused on the fact that although people in the United States often try to lose weight, statistics show that the general population has gained weight, on average, during the last 10 years. A researcher hired by a weight- loss organization is interested in determining whether three kinds of arti?cial sweet- ener currently on the market are approximately equally effective in reducing weight. As part of a study, a random sample of 300 people is chosen. Each person is given one of the three sweeteners to use for a week, and the number of pounds lost is recorded. To reduce experimental errors, the people in the sample are divided into 100 groups of three persons each. The three people in every group all weigh about the same at the beginning of the test week and are of the same sex and approximate- ly the same age. The results are SSBL = 2,312, SSTR = 3,233, and SSE = 12,386. Are all three sweeteners equally effective in reducing weight? How con?dent are you of your conclusion? Discuss the merits of blocking in this case as compared with the completely randomized design.