The transportation research division of a northern state is examining the amount of road damage associated with various methods used to clear snow and ice from the roadways. The division engineers have selected two levels of each of the following substances that are applied to the roadways: sodium chloride, calcium chloride, and sand. The response variable measured on each of the treated roads is the number of new cracks per mile of roadway. Because traffic volume is highly variable and could impact the response variable, the engineers decide to use a randomized block design with the traffic volume during the previous winter as the blocking factor. Each of the six treatments is randomly assigned to five roadways. The data are given here.

a. Write a statistical model for this experiment.
b. Use a profile plot to display the interaction between treatment and level.
c. Perform appropriate F tests, and draw conclusions from these tests concerning the effect of treatment and level on the mean number of cracks.
d. Use a normal probability plot and a plot of the residuals to determine if there are violations in the appropriate conditions for validly drawing conclusions from the F tests.

Transcribed Image Text:

Sodium Chloride Calcium Chloride Sand Roadway Lo High Low High Low High 37 43 42 47 45 56 47 48 50 54 63 27 27 36 50 31 37 37 48 57 45