Qusetion: The researcher mentioned in Exercise II proceeds to randomly assign a type of paint to each of the four locations. It is known that specific aspects of each location (e.g., traffic volume and road conditons) also affect the duration of the reflectivity of the paints. Comment on whether or not the above allocation of paints (treatments) to the road segments (experimental units) will avoid confounding with the treatment effect with the location factor. Explain your answer and describe a possibly better allocation of treatments to units.
Exercise II: The researcher in charge of the study described in Exercise I identifies four locations of the highway, and for each location she designates four sections of length six feet to serve as the experimental units on which the paints will be applied. It is known that specific aspects of each location (e.g., traffic volume and road conditions) also affect the duration of the reflectivity of the paints.
(a) Does this change the number of populations involved in the study?
(b) List the factors involved in this experiment, the levels of each factor, and the treatments.
Exercise I: Rural roads with little or no evening lighting use reflective paint to mark the lanes on highways. It is suspected that the currently used paint does not maintain its reflectivity over long periods of time. Three new types of reflective paint are now available and a study is initiated to compare all four types of paint.
(a) How many populations are involved in the study?
(b) What is considered a treatment in this study?
(c) Letting µ1 denote the mean time the currently used paint maintains its reflectivity, and µ2, µ3, and µ4 denote the corresponding means for the three new types of paint, write the control versus treatment contrasts.