A university in a large urban area is having a major problem with traffic congestion. A study

Question:

A university in a large urban area is having a major problem with traffic congestion. A study was funded to determine the volume of traffic on campus streets by cars that are not associated with university business. One small phase of the study involved obtaining daily counts on the number of cars crossing but not making use of campus facilities. Video cameras were placed at each entrance to the university. The license plate number and the time of entrance or exit for each car passing through the campus entrances were recorded. Using these data and allowing a reasonable time for cars to traverse the campus, the researchers were able to determine the number of cars crossing the campus but not making use of any campus facilities during the business day. A random sample of 12 weeks throughout the academic year was used in the analysis. During each of the 12 selected weeks, the traffic volume was recorded during the business hours of the five days. The data are given in the following table.

a. Write an appropriate linear statistical model for this experiment. Identify all the terms in your model, and state all the conditions that are imposed on these terms.
b. Display a complete analysis of variance table, including expected mean squares, F tests, and p-values.
c. Estimate the variation in the mean weekly traffic volumes across the year using the information in the AOV table.
d. Is the variation in traffic volume within weeks greater or less than the variation in mean weekly variations across the year? Justify your answer using the estimators of the variance components obtained from the information in the AOV table.
e. Use the residuals from the fitted model to determine if there are any violations in the conditions necessary to conduct the tests of hypotheses in this experiment.