The Phoenix, Arizona City Council was approached several years ago by a firm that wanted to lease the City red-light cameras to install in intersections. In exchange for a portion of all of the fines collected from red-light violations, the firms would set up cameras that would take a photo of the license plate of any car that entered into the intersection after the light had turned red. The City then could mail out a citation to the offender. The goal of the program was to not only yield some added revenue for the City but also to reduce the number of accidents due to cars speeding through red lights.

The City Council, nevertheless, was a bit wary of the vendor because they had heard that in other cities citizens were displeased with the program. Moreover, their analysts had found evidence that red light cameras may actually increase the number of accidents because drivers end up slamming on the brakes when the yellow light comes on leading to a rear-end accident if the car behind them was caught by surprise.

Consequently, the City Council astutely decided to conduct a preliminary experiment before agreeing to a contract with the red light camera vendor. It identified 80 intersections controlled by red-lights that also experienced a heavy amount of traffic. These intersections were a mix of intersections in the heavily travelled downtown core of the city as well as other intersections in the outskirts of the City. It had its staff randomly place each intersection into one of two treatment groups:

• Group 1 40 intersections were left as they were to act as the control group.
• Group 2 40 intersections had red light cameras installed.

The data collected in these experiments are provided in the Excel spreadsheet. The variables are:

Experimental Condition: Group 1 (Control) No Cameras; Group 2 (Experimental) Cameras

Accident in Pretest Year: Total number of accidents recorded in the intersection in the year prior to the beginning of the experiment

Accident in Test Year: Total number of accidents recorded in the intersection in the year during the experiment

Your assignment is to analyze these data for the City Council to see whether the red-light cameras seem to affect the number of accidents.

• Calculate the average number of accidents for the control group and experimental group of intersections in the test year. (Post-test only comparison). What do you observe?
• You want to be sure that your conclusion is statistically valid. So, you will need to conduct a hypothesis test comparing each group (experimental and control) using the test year data only. State the null and alternative hypotheses for this test.
• Conduct a one-tailed t-test: Two samples assuming unequal variance using Excel, an online statistics calculator or by hand. Are you able to reject the null hypothesis, again, just looking at the test year results? In responding to this, reference the p value associated with your t score, state alpha, and interpret your hypotheses based on your results.
• As an analyst, you arent so sure this was the best way to go about things, so you decide to calculate the difference between the pre-test number of accidents and the test-year number of accidents for each intersection. What is the average change in the number of accidents for the control (Group 1) versus the experimental group (Group 2)?
• Conduct another hypothesis test to check whether this difference is statistically significant between the control and experimental groups. Again, state your null and alternative hypothesis, conduct the same type of t-test, and interpret your results.
• Do the results of your hypothesis tests in parts #3 and #5 agree? Explain why they do or do not lead to the same conclusion. Based on what we learned at the beginning of the semester regarding study validity, which of the two tests is giving the most useful results? Why do you think that?

Group 1 - Control (No Camera) Accidents in Accidents in Pretest year Test year Test year 10 20 25 7 17 23 16 24 Group 2 - Experimental (Red Light Cameras) Accidents in Accidents in Pretest year 6 5 18 17 19 12 16 11 16 15 5 4 15 14 11 8 16 16 18 14 21 19 19 23 11 16 17 21 13 14 15 20 23 23 17 24 16 26 14 26 6 15 5 8 15 18 19 9 11 13 10 10 12 22 12 12 18 13 7 10 6 9 5 18 11 9 11 5 12 11 10 16 11 15 6 17 5 5 9 7 8 11 10 24 8 11 13 9 5 17 27 19 29 4 10 12 8 5 25 7 27 10 19 22 23 10 21 10 16 8 8 17 6 5 14 18 10 10 7 9 27 12 8 19 24 26 11 7 18 17 8 12 9 19 16 5 18 16 16 6 5 5 6 20 11 16 12 6 4 4 25 26 Group 1 - Control (No Camera) Accidents in Accidents in Pretest year Test year Test year 10 20 25 7 17 23 16 24 Group 2 - Experimental (Red Light Cameras) Accidents in Accidents in Pretest year 6 5 18 17 19 12 16 11 16 15 5 4 15 14 11 8 16 16 18 14 21 19 19 23 11 16 17 21 13 14 15 20 23 23 17 24 16 26 14 26 6 15 5 8 15 18 19 9 11 13 10 10 12 22 12 12 18 13 7 10 6 9 5 18 11 9 11 5 12 11 10 16 11 15 6 17 5 5 9 7 8 11 10 24 8 11 13 9 5 17 27 19 29 4 10 12 8 5 25 7 27 10 19 22 23 10 21 10 16 8 8 17 6 5 14 18 10 10 7 9 27 12 8 19 24 26 11 7 18 17 8 12 9 19 16 5 18 16 16 6 5 5 6 20 11 16 12 6 4 4 25 26