Decide whether each of the following is using the FEM or the REM.
a. A professor is trying to select a textbook for a sociology course from 4 different ones which are available. He divides his students at random into 4 groups and assigns the textbooks to the groups at random. After using the different books for the course, all students still enrolled take the same examination. ANOVA is used to analyze the results.
b. A manufacturer builds a piece of equipment to turn out machined parts. To study the performance of her machines, she selects 8 machines at random and then selects 10 parts at random from the production of each of these machines. She measures the lengths of the 80 pieces and performs an ANOVA.
c. An educator wishes to study the competence in algebra of all New York City students who have just completed the ninth grade. Five junior high schools are selected at random, and within each school a random sample of ninth-grade students are given examinations. Using these scores, the hypothesis that there is variability among the schools is tested.
d. Worms are classified into three groups by a structural characteristic: small, medium, or large ventral flap. Three random samples of 11 worms are taken from each group and the weight of each worm is recorded. The hypothesis is tested that the mean weight of each group is the same.
e. A psychologist devises an examination in such a way that the final score depends almost entirely upon the ability of the subject to follow instructions. The test is given to 40 students who have been divided into 4 equal groups at random. The instructions are given in the following 4 ways:
Group I written and brief
Group II oral and brief
Group III written and detailed
Group IV oral and detailed
An ANOVA is performed.