Question

A traffic engineering study on traffic delay was conducted at intersections with signals on urban streets. Three types of traffic signals were utilized in the study: (1) pretimed, (2) semi-actuated, and (3) fully actuated. Five intersections were used for each type of signal. The measure of traffic delay used in the study was the average stopped time per vehicle at each of the intersections (seconds/vehicle). The data follow.

Pretimed	Semi-actuated	Fully actuated
36.6	17.5	15
39.2	20.6	10.4
30.4	18.7	18.9
37.1	25.7	10.5
34.1	22	15.2

1. Conduct an analysis of variance for the data, and estimate the following contrasts and their standard errors:

1. a contrast between the pretimed and the average of the semi- and fully actuated signals
2. a contrast between the semi- and fully actuated signals

2. Compute the sum of squares of each contrast, and show that their sum is equal to the treatment sum of squares in the analysis of variance.
3. Test the null hypothesis in part (c) with the F test at the .05 level of significance.

Answer 1