University of Guelph STAT*2230 Assignment (8) Question (1) (6 marks) An important factor in road safety on rural roads is the use of reflective paint to mark the lanes on highways. This provides lane references for drivers on roads with little or no evening lighting. A problem with the currently used paint is that i does not maintain its reflectivity over long periods of time. A researcher will be conducting a study to compare three new paints (P2, P3, P4) to the currently used paint (P1). The paints will be applied to sections of highway 6 feet in length. The response variable will be the percentage decreases in reflectivity of the markings 6 months after application. There are 16 sections of highway, and each type of paint is randomly applied to four sections of highway. Suppose the researcher conducts the experiment as described. The reflective coating is applied to the 16 highway sections as in the table below: Section 2 11 12 1 Paint P P P P 16 13 9 3 14 5 8 7 15 10 4 6 P2 P2 P2 P2 P3 P3 P3 P3 P4 P4 P4 P4 Six months later the decrease in reflectivity is computed at each section. The resulting measurements are given in the table below: Paint Pl 26 33 25 19 P2 19 34 23 16 P3 24 36 25 15 P4 14 23 20 16 Is there significant evidence at the a -0.05 level that the four paints have different mean reductions in reflectivity?